A proposal to build a veterinary school at the University of Maryland's Eastern Shore branch picked up support from university officials yesterday.

Frank L. Bentz Jr., vice president for agricultural affairs, told members of the Senate Finance Committee that the university would prefer setting up a regional school in cooperation with the state of Virginia.

But he said the university also would consider going ahead on its even though it would be less expensive both to build and to operate a veterinary medical school in cooperation with another state.

The testimony from Bentz came at a hearing on a bill to require the State Board for Higher Education to develop a plan for a regional veterinary school.

The board has in the past opposed creating a vet school in Maryland, saying it would be too costly and would use money needed in other areas of higher education.

But Fred C. Spigler, a staff aide to the board told the committee Wednesday that the board probably would not object to a regional school.

Reading a statement from Sheldon H. Knorr, state commissioner for higher education, Spigler said that board studies do not justify the major expenditures that would be necessary to establish a complete vet school in Maryland.

The statement also said there is a danger of turning out too many veterinarians, and predicted that the number of vet school graduates throughout the South will hit 700 by 1985, compared with just 350 in 1975.