(written from a Production point of view)
Until the re-invented Star Trek film of 2009, Star Trek: Insurrection, tied with TNG: "The Best of Both Worlds, Part II", and Star Trek: First Contact, has been, after Star Trek: The Motion Picture, which holds the record with nine introductions, the Star Trek live-action production that introduced the most new space faring designs at once, eight each, the Type 11 shuttlecraft being one of them.
Though the script for Insurrection did not call specifically for a new shuttle design, a new one, carried aboard the USS Enterprise-E, was designed, as it was so instrumental for the scene where it battled the Federation mission scoutship. John Eaves, credited as Illustrator for the feature, and the actual designer of the vessel, noted, "For the shuttle, I just tried to follow the Enterprise lines, so it's got a real sleek, aerodynamic look. The aerodynamics don't really matter to the space part of it, but when it is in atmospheric flight, you get a real nice dimension – a kind of corvettey, kind of streamlined look – that echoed the Enterprise. That's where that shape came through.(...)At one point we were thinking about kind of making a unifold out of the shuttle, so the traditional nacelles were folded within the shape of the ship. It didn't look as good. It had a nice look to it, but it didn't say 'shuttlecraft' like having the nacelles separate does, so we went with a more traditional yet real streamlined look to it. We also went with the standard colors that had been used on TV and in the last film, so it has that kind of beige-tan color." (Star Trek: The Magazine Volume 1, Issue 4, p. 29) Eaves has added, "The previous shuttles were a bit more stocky, sort of designed to match the Enterprise-D, with that really rounding kind of organic flow to it. But this one has more of an aerodynamic design, like the E. It's much more streamlined, kind of speed-car design to match the new Enterprise's sleekness." (Star Trek: Action!, p. 190) and, "I repeated certain shapes throughout the Federation designs, so the ships all seemed to extend from a single technological base." (Cinefex, issue 77, p. 72)
Eaves has also been on record as having stated, "We also had a new shuttle we got to design. We kind of based them roughly on an aerodynamic shape, but with the traditional small struts and the nacelles on it, like the older shuttles. When you carry over that architecture a little bit, then it's still old, though still gets a new sense into it, with the streamline into it of the Enterprise-E, we wanted to be very specific that they were Enterprise-E shuttles." (Star Trek: Insurrection (Special Edition) DVD-Special feature "Production:The Art of Insurrection") A subtle variation was performed by Eaves on his designs, in order to establish a continuity between the new Federation vessels, "What we started doing on this movie was putting the hatch on the very back of all the ships [remark: as opposed to also having side hatches on previous shown smaller craft] - the shuttle, the yacht, Data's scout ship; they all have the hatch on the back." (Star Trek: The Magazine Volume 1, Issue 4, p. 30) Eaves, according to the annotations on his design sketches, has worked on the design from January through March 1998.
Eaves re-visited his design as he has included four shuttles of this type in the shuttlebay of the Enterprise-E in the December spread of the Star Trek: Ships of the Line (2011) calendar. One of these shuttles is named the Galileo, and it was there he coined the type designation. 
For Insurrection, the producers decided to complete the transition into the digital realm and that this feature would be the first movie completely without the time honored motion control model photography. However, in this stage of the technique, that meant that the CGI-workload had to be divided between two VFX-houses, Santa Barbara Studios (SBS) for the outer space shots, and Blue Sky/VIFX for the planet bound effects. As the Type-11 shuttlecraft first appeared in outer space, the model and effects of it were executed for this film by Santa Barbara Studios in the Maya CGI software. (Sci-Fi & Fantasy Models, issue 34, p. 29) A relatively early outing at the time into the realm of CGI, solicited the following remark of Eaves, "The CGI guys needed every possible line drawing. They wanted all the details in advance–which differed from the way I usually work with traditional modelmakers, leaving areas open for them to contribute. But Santa Barbara did not want to have to go through an approval process on every aspect of these ships–which made sense, because there wasn't time to make that happen while still getting the ships modeled and animated and rendered out. It was a learning experience for me to provide these detailed technical drawings." (Cinefex, issue 77, p. 72) Detailed scale comparison charts, originating from this desire has made Eaves set the in-universe dimensions of the Type-11 shuttlecraft at 54×29 feet.
No physical counterpart is known to exist.
The docking clamp scene
In Scene 67-78 of Insurrection, a situation was described where the shuttle and Data's scout ship are literally locked together in a fight. In the early stages of the script development, it was not clear on which side the shuttle would dock, so Eaves in his designs took into account of putting docking equipment on both the dorsal as well as the ventral side of the shuttle. (Star Trek: The Magazine Volume 1, Issue 4, p. 30) As Eaves said, "We have a scene where the shuttle has a magnetic lock and has to dock onto the ship, so they do this maneuver. Throughout, they had to have these really heavy locks to lock the two ships together, while they have access to ports, and so on both ships we had designed the same types of emergency hatches, that are based on circle hatches like manhole covers, so we had them on the bottom of the shuttle, as well as on Data's scoutship. So, no matter how they wanted to put it visually together, they could dock on top, dock on bottom, depending on where they wanted to do the visual, what would be more exiting in the film. That is kind of how we based the placement of the hatches." (Star Trek: Insurrection (Special Edition) DVD-Special feature "Production:The Art of Insurrection") Eventually, it was decided to have the shuttle dock from below, much to the delight of Co-producer Peter Lauritson, who commented, "There is is one shot in particular that I really liked where we are looking down and we're seeing Data in the cockpit of his ship and we tilt down of him, and we see Picard and Worf, sneaking up below him from the other cockpit." Once decided upon, the scene was storyboarded by Ray Harvie (Star Trek: Action!, p. 193), and eventually executed as mostly CGI, entirely by SBS, even though some of the sequences were planet-bound.
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Lauritson further elaborated on the scene, "One of the things we wanted to do with the sequence, was have these ships doing a lot of intricate maneuvers and swoops and spins, and things like that. And that was something that would be extremely difficult with Motion control photography, so it was another advantage we had by creating the ships CGI. Normally we're up in space with these ships and we can create whatever background we want. In this case we're coming down into the atmosphere, so we hired a jet, you know, with a camera rig and went up on a semi-stormy day, and photographed these clouds backgrounds, and had to guesstimate the kinds of moves and things that we would want to see in the background of these ships, so that it would help sell the CG ships in a real atmosphere." Continuing to the final sequences, Lauritson added, "When the ships go into a spin, going down toward the surface, imagery was, some of it was CGI, but it was all created by referencing the real landscape we were at, and that was a ranch outside of Santa Barbara. For that final shot, where the ships swoop down and come very close to earth and the grass is kicked up into the netherlands. We had a helicopter do a swoop pass, as if it were these ships. We did not came as close as them, of course, but it did make the grasses move the right way, and then for that final kick of grass into the lands, that was CG." (Star Trek: Insurrection (Special Edition) DVD-Special feature "Creating the Illusion:Shuttle Chase")
"We used real flame for the reentry heat texture map, then warped that over some cone geometry and rerendered to get the reentry heat look. We would multiplane the edges to keep from getting that crispy CG look, then cycle the textures through quickly, sometimes enhancing them with backlit nitrogen streams or particle animation work.", SBS's Animator Mark Wendell proudly recalled. Lauritson had with him in the Lear jet, cinematographers Clay Lacey, and in the helicopter Kevin LaRosa for the live footage. SBS nevertheless had to perform a number of color corrections in order to match up the elements shot, with the planet's greener-than-green appearance. Still, the more dynamic, plunging towards the earth plate-shots, could not be achieved with the aerial footage, needing another approach. Editor James Strauss combined cloud elements with Richard Kreigler's digital matte paintings to create a multiplane environment in the SoftImage software through which the camera could travel. However, taking it up a notch, as Wendell explained, "To take it one more step, we took advantage of Nothing Real's Shake software, which let us comp the ships by dilating the matte to take the edge off. Shake let us play with blur and opacity factors and really marry these two craft into the background, even to the point that the TD could add grain himself" (Cinefex, issue 77, p. 80)