The wisp ship was a starship inhabited by non-corporeal beings who were described as "wisps" by the crew of Enterprise NX-01. Although the wisps who inhabited the ship were said to live in subspace, they relied on the ship so as to not be exposed to normal space, which they could not normally inhabit.
The ship had a forward, ovoid hatch that split into several pocketed sections; the surrounding hull formed a pronounced ventral "sill" with two projecting spines.
This ship was capable of traveling at speeds of up to at least warp 6, yet emitted no warp signature that Enterprise could detect. During Enterprise's encounter with the vessel, the crew of the former craft were unable to identify the composition of the wisp ship's hull, nor locate a transceiver. The ship was at least 500 meters wide, and had the ability to neutralize Enterprise's phase cannons and spatial torpedoes, and warp and impulse engines after it had taken the ship into its bay. Once inside, Enterprise's sensors were unable to penetrate the hull to determine whether or not they were still at warp.
The wisp ship was encountered by Enterprise in 2152, approximately 150 light years from Earth. After several of Enterprise's crew were forcibly inhabited by the wisps, it was eventually determined that their ship was deteriorating, and they had no way to repair it. Since they couldn't survive in space, to save themselves, eighty-two of the hundreds aboard decided to make the "crossing," and take over the bodies of each of the crewmen on Enterprise, while the rest would try to find another vessel of corporeal beings.
Unfortunately for them, their plan failed, and Enterprise was able to release the possessed crew members before firing two spatial torpedoes into the opening of the wisps' ship. Consequently, the wisp vessel was destroyed, allowing Enterprise to escape. (ENT: "The Crossing")
In the final draft script of "The Crossing", the "giant" wisp ship was described thus; "The vessel is otherworldly, with a shape unlike any vessel we've seen." The opening in the craft was described as "a large, maw-like portal [...] on the forward hull." The inside of the craft, which was commonly referred to simply as "alien vessel", was described as a "dark, Giger-like interior," referencing artist H. R. Giger, and as a "vast, strange landscape." There were also intended to be "tiny nodules embedded in the ceiling" and a subsequent scene description commented, "The floor is neither level nor flat [...] [with] various structures [built into the floor]."
"The joke with this one is that all my files are labelled 'NBS'. That would be for the producers' request for something 'Never Before Seen'. I had to laugh right up front because I knew that that's really not what they wanted. Anything too different ran the risk of 'confusing the audience'. Since they asked, I'd start out at the far end of the weirdness scale. In the script, Enterprise is described as 'caught' by a very alien looking spacecraft. I visualized the Enterprise being attacked by an insect. I had once watched a spider jump on its prey and devour it, so that's what I was thinking. I had a CG parachute that I had modeled a while back. I applied distortion maps to it until I found a form that was sufficiently 'creepifying' and pleasing. There was no way that design would ever happen. I was asked to make more of a ship, and with a distinct maw... but... um... different. I kept it organic, but gave it a distinct metallic feel. Up front the ship extended enormous petals, like a sea anemone, to pull in its catch of the day. Well... they couldn't tell which direction this was meant to go, so it was no good either. I thought that usually the audience could tell what direction the ship went by the direction the ship was going? Maybe it was feared that you would think it was flying backwards. Hey! If you want something different, you have to buck the conventions. Either way, Thursday came every week, and I was having the best time! [The next one] was more of a ship with direction, but [...] word came down that the maw was getting lost (what about its paw?). Nothing gets thrown away, and I recycled this later as the Xindi Reptilian ship. Everything stripped away but the maw. These were sent to Eden. They may have gone with additional sketches by John, but I can't remember." 
John Eaves took another approach to the design:
"So anyway, the ship went through a few changes, and the first version has the Jem'Hadar cruiser's lines as the understudy and some heavy organicasizeing on top. I took the borgifying approach for the first pass. Rejected brutally. Ship two followed with a tendrilled beetle bug look... also rejected heavily. Which lead to version three which is a modified fish/doomsday machine combo!!! Again the big axe fell, and version #4 came to be... they sorta liked the underlying shape, and had me do a pass minus the tendrils and up the scale with the addition of more patterned detail, as opposed to total organic randomness. Thus the final drawing came to be, and they even drew a happy face with a little star on the corner of the page!!" The producers chose the design John Eaves tendered in January 2003. At Eden FX, Dan Curry worked with modeler Pierre Drolet to finetune the design where it was converted into a CGI model. The interior of the wisp ship was modeled after a design of Drexler. (citation needed • edit)