Since his early days in high school, Joe Wells of Buchanan, Va., has wanted to be a veterinarian, but in recent years the competition for spaces in schools of veterinary medicine has grown so intense that he figures he needs a fallback position.

"If I don't get into veterinary school, I'll probably go to medical school and become a people doctor," says Wells, now a pre-veterinary student at Virginia Tech in Blacksburg.

There is good reason for Wells to be anxious about his choice of career. This year he'll be one of 300 candidates competing for 31 slots in veterinary school available for Virginia residents.

Nationally, it's estimated there are at least six qualified applicants for every space available in veterinary schools and interest in veterinary medicine has soared to the point where such schools are statistically more difficult to get into than medical schools.

"We've had one or two students every year for the last five or six years who went to medical school because they couldn't get into veterinary school," said Robert Hammond, chairman of veterinary sciences at the University of Maryland.

Partly to accommodate the rising number of would-be veterinarians and partly to deal with a veterinarian shortage in rural areas, both Maryland and Virginia took initial steps this month toward establishing schools of veterinary medicine.

In Virginia, the state's Council for Higher Education authorized planning for a veterinary school at Virginia Tech, contingent on the receipt of federal matching funds and foundation money. Richard Talbot, dean of veterinary sciences at Virginia Tech, says he'd like to enroll the first class of 50 students by the fall of 1979.

In Maryland, the board of regents of the University of Maryland has given priority to a feasibility study into the establishment of a school of veterinary medicine at the University of Maryland Eastern Shore. Both schools would have curriculums that stress training in the care of large farm animals.

Ironically, the surge of interest in veterinary medicine - fueled in part by an increasing number of pet owners - has been accompanied by a shortage of veterinarians in rural areas.

"Most veterinarians would rather look at dogs and cats that are brought into their office than treat horses and cows when they've got to get in their car and drive out to see them," said Barry Dorsey of the Virginia Council for Higher Education.

"We have a lot of veterinarians. But there are very few veterinarians who will practice on large animals. They can make a whole lot more money seeing pets where the people bring the animals to them," said Norman Coyner, who runs a dairy farm in Fauquier County, Va.

"Right now, if I had a real sick animal, the best thing for me to do would be to load it onto a truck and drive it 25 miles to Tappahannock or Ashland," said James Townsend, who operates a dairy farm in King William County, about 20 miles outside of Richmond.

Up until 1970, Townsend said, he was able to get veterinarians from Richmond whenever one of his cows needed veterinary services.

"Around 1970 they told us they were only interested in looking after dogs and cats," said Townsend.

Currently Townsend has a veterinarian on retainer from Petersburg - 50 miles away - and he gets monthly visits on a regular basis. But in an emergency, it can be catch-as-catch-can, and he does remember loading a low into the back of a truck once for a 25-mile drive to the closest vet.

Both Maryland and Virginia currently train veterinarias by sending them to schools in other states and subsidizing the bulk of their tuition expenses. But the number of such veterinary students has doulble in the past few years and oficials are afraid the other states will balk at accepting more and more Maryland and Virginia residents.

Martha Moon of Rockville for example, is in her first year at Ohio States's School of Veterinary Medicine, and the state of Maryland pays Ohio $6,000 to subsidize Moon's tuition.

Moon pays $640 a quarter, the same as she would be paying if she were a resident of Ohio. She is one of 29 Maryland students to enter veterinary school each year under agreements Maryland has with Ohio State, the University of Georgia, Tuskegee Institute and the University of Florida.

"I've always loved animals and I've always known my career would have something to do with animals," Moon said.

Wendy Furie of Frederick is currently at the University of Florida veterinary school, paying $449 a quarter while the state of Maryland pays $5,000 for her veterinary training. "I've had horses and dogs all my life and I guess I've chosen veterinary medicine all along," said Furie.

The 31 Virginia residents to enter veterinary school each year do so under a similar arrangement as those from Maryland, with the state subsidizing the bulk of their tuition. It's estimated that about half of the Maryland and Virginia veterinary students return to practice in their home areas.

Interest in veterinary medicine has been growing for a long time, "but it seems to have really surfaced in the last half-dozen years," said L. West, director of scientific activities for the American Veterinary Medical Association.

"As the profession becomes more visible more people become attracted to it as a career," said West, adding that he thinks publication of the best seller "All Creatures Great and Small" and by veterinarian-author James Herriot in 1972 has something to do with the trend.