Holding her sleepy 5-week-old daughter, April, tightly in her arms, Evelyn Burke says, "I'm glad I did it. Two babies are enough."

Last Jan. 13, the same day April was delivered by cesarean section at Johnston Memorial Hospital here, the 22-year-old Mrs. Burke had a voluntary sterilization operation, ending her childbearing days forever.

The Burkes were afraid a furture pregnancy might mean another, potentially dangerous cesarean. "I don't believe that when God said be fruitful and multiply, He said kill your wife," says her husband, Don.

But the Burkes concede they had another reason for their decision: money. "If I could afford them [children], I wouldn't care if I had 35," says Don Burke, a $2-an-hour farm laborer whose yearly income puts him well below the poverty line. As it was, the couple opted for sterilization -- with the help of the state of Virginia, which paid the entire $700 cost of the operation.

The Burkes are typical of hundreds of couples here in rural, impoverished southwest Virginia -- where large families have been a fact (and a way) of life since pioneer days -- who have availed themselves of a low-profile state program of free, voluntary sterilizations for poor people.

Begun in the mid-1970s to aid families who could not meet the strict guidelines for Medicaid-funded operations, the program, administered by the state health department's Family Planning Bureau, last year spent $636,158 for 1,021 such operations. Only Texas spent more.

While the program is available throughout the state, most of the sterilizations occur in areas like this one. Washington County, including the county seat of Abingdon, had more in 1980 -- 26 -- than Fairfax County, Arlington and Alexandria together. State family planning officials say fewer people in urban areas meet the income restrictions for free operations.

State officials, anxious to avoid provoking religious or other critics and mindful of last year's scandal in Virginia involving involuntary sterilizations at state-run mental institutions, are careful not to promote their efforts (they stress it is strictly voluntary.) Still, the idea has gained steadily in popularity.

"I would say it has to do with changing cultural values," says Dr. D. Craig Smith, medical director of the district that includes Abingdon. "It [sterilization] is very effective and people see how easy it is. Once it gets going in an area, it tends to fuel itself. It's a good method that's got a bad name."

Along the way, it has begun to reshape decades of family tradition in the mountainous farming country here.

The Burkes, who live on a dairy farm a few miles outside of Abingdon the seat of Washington County, both were familiar with life in a big family. Evelyn was one of five children. Don, 32, was one of six. But with Susanne, 21 months, and little April, the Burkes were determined to call a halt.

Sometimes, says Don Burke, his weekly income is as low as $14 when there is little work to do on the farm. His total income in 1980 was $1,169 The unpaid doctor and hospital bills from his wife's two cesareans total $6,000. His 1969 Plymouth needs a minimum $600 in repairs to keep running.

"You can see why we don't want to have any more children," he says.

After counseling with the Family Planning Bureau clinic in Abingdon, the couple settled on sterilization, deciding the pill and other conventional methods were either too risky medically or not reliable enough. Evelyn decided to have the operation because Don was "too shy" to have a vasectomy.

(Family planning officials acknowledged that only a handful of men have opted for vasectomies, which, at $120, are almost six times as cheap as the tubal sterilization for women.)

Because the Burkes' income was less than 80 percent of the state median, the bureau paid the $700 cost of the operation, usin a special allocation for that purpose from the state welfare department.

"From a strictly economic point of view," says Dr. W. David Fletcher, a member of the state health board, "it probably costs less than it would for the state or federal government to deliver a child and pay for its support."

Few states, including the District and Maryland, have followed Virginia's example. "As commissioner, I would not advocate it," says D.C. Social Services Commissioner Audrey Rowe. "It can be abused too easily." But Virginia officials like Family Planning Bureau chief Donald Foster disagree.

"We think poor people should have the same opportunity as the more well to do," he says.

Steve Calos, a former bureau employe who is now with the Virginia Employment Commission, says some blacks expressed concern in the 1970s that the program might be used to reduce the state's minority population. But they dropped their objections, according to Calios, when it turned out those seeking sterilization were predominantly white.

Even so, state health and welfare officials continue to step softly, wary of stirring criticism.

The Moral Majority, the bastion of the New Right in Virginia, opposes publicly financed birth control aid for minors without parental permission, but spokesman Cal Thomas in Lynchburg says, "We have no position on voluntary sterilization. We are not physicians or lawyers."

The Moral Majority's leader in Washington County, the Rev. Tom Williams, pastor of Emmanuel Baptist Church near Abingdon, has been a vocal opponent of such social issues as limited Medicaid funding of abortion and "pornographic" books in the local public library. But he hasn't had a word to say publicly about the county's family planning program, which, in all its aspects, has 1,000 clients, about 20 percent of them minors (who, under state law, are entitled to counseling and free birth control aids without parental permission).

Williams, in an interview, said "I don't approve of the program. I don't think federal or state funds should be used for this purpose. But there's a limit to what one man can do. My wagon is pretty well loaded."

Meanwhile, word about the program continues to get around.

Carolyn J. Lange, a senior at Virginia Intermount College, a Baptist-affiliated school in Bristol, a city on the Tennessee border, was waiting until she turned 21 so she could be eligible. Two weeks after her 21st birthday on Feb. 7, she filled out her application in Bristol. After a 30-day waiting period (to give applicants a final chance to change their mind), she can have the operation.

Lange, an A student studying medical technology, is unmarried and has a quarter-century of child-bearing potential before her. But still wants to be sterilized. "I feel my brother and sister before me replaced my parents. I consider myself excess population."

Two of the newest clients of the Washington County family planning program are Debbie and Gary Thompson, Debbie was one of 14 children, Gary, one is six. They get by on Gary's $538 monthly salary in his new job at the county landfill.

After their second baby was born last year, they decided they couldn't afford any more children. The pill was ruled out because Debbie had some gall bladder problems and had contracted yellow jaundice. So Debbie chose to be sterilized.

"We thought about it over and over," said Gary, "and didn't see any other way."