While undergraduates know “Swing Space” as the stand-in dorm for whichever residential college is under renovation, for the staff of the University Art Gallery, every space is in swing.

Susan Matheson, the gallery’s acting director, used to have her office in the Kahn building of the Art Gallery until it started renovations in 2005. Now she works at 341 Crown St. As the older Swartwout wing of the gallery will undergo renovations, the staff housed there will take over 341 Crown, and Matheson will move to 900 Chapel St. — an off-campus office building on the New Haven Green.

“We’re in a musical chairs moment,” she said.

It’s not just the gallery staff, either. Across the University, finding office space during renovation, construction and expansion has become a constant and complex shuffle. The demand for new spaces is fast catching up to the supply, and relief is unlikely to come until new offices are completed in about five years, administrators say. In the meantime, the administration is scrambling to find a place for everyone, including by renting off-campus office space at an unprecedented level.

It is like a giant version of the puzzle where you have to slide the tiles around one empty space, said J. Lloyd Suttle, deputy provost for undergraduate and graduate programs. And then add more tiles.

Suttle, who receives three or four requests for new spaces every week, said he does not want to get to the point where departments cannot hire new staff simply because there’s no physical place to put them. But office space is very tight, and a serious shortage is developing.

In some ways it is a good problem to have, Suttle said. Provost Peter Salovey said the faculty has grown in recent years and will grow more as Yale College expands with the two new residential colleges.

“Faculty office space is currently very tight on this campus, and we need to be creative about finding or developing new spaces,” he said in an e-mail message. “This may include renting spaces off campus as well.”

While the new residential colleges add to the demand for new faculty and therefore new offices, they also displace some existing buildings for the political science and sociology departments. The political science department will move across Prospect Street to new Rosenkranz Hall, but the administration has yet to find an interim home for the social sciences library or the sociology department while the new colleges are being built, Suttle said.

Sociology professor Hannah Brückner said, knowing the shortage of office space, that she is concerned she and her colleagues will spend years in temporary spaces scattered across the campus.

“It makes it kind of hard to be a department,” she said of the potential diaspora.

The top priority, Suttle said, is to keep faculty and other officials who interact with students on a daily basis closest to central campus. So the University is squeezing more people into its existing spaces, in some cases converting storage spaces into offices.

New buildings like Rosenkranz will help, Suttle said, and the situation will eventually settle down when some of the University’s $2.6 billion construction projects come online in the next four years. Eventually, the new School of Management campus will free up the offices SOM currently occupies in mansions on Hillhouse Avenue.

But that’s several years away. The challenge is between now and then, Suttle said.

The priority for faculty explains why some administrative offices have already resettled off-campus. The Development Office is located in 157 Church St.; the Office of Public Affairs has a suite in the high-rise at 265 Church St.; and two floors of the office building at 110 Whitney Ave. are occupied by the Beinecke Library, SOM and the International Security Studies Program.

About 650 staff members from Yale’s information technology services, finance, budget, business services and other departments are in the process of moving their offices from 155 and 175 Whitney Ave., making way for the new SOM campus, to 165,000 square feet of rented space at Science Park.

Matheson said she actually preferred the off-campus location because it would be closer to the Art Gallery than on-campus alternatives on, say, Science Hill. Proximity and cohesion is important to the gallery’s staff, she said.