Donna Murphy, the registrar at Bishop Denis J. O'Connell High School in Arlington, has a backlog of applications for admission to the school that would ''triple or quadruple'' the 1,612 enrollment.

Murphy said she gets calls nearly every day from parents asking to have their children put on the waiting list for the Catholic school. But one recent call surprised her.

"It was from a mother whose child was in kindergarten, and she wanted to put the child on the waiting list to make sure her child could come here when it came time for high school," Murphy remembered.

When Aquinas School, a Catholic elementary school in Woodbridge, opened in 1977 with 290 students, it was already too small to accept all those wanting admission. Since then the 610-student school has added a wing, nearly doubling its size and enabling it to house two classes for every grade.

But Sister Christine, the school principal, said there is still a waiting list of nearly 35 applicants for some grades. "A new (grade) school has opened up (in the Woodbridge area) almost every year I've been here," she said. "It's astounding."

Catholic school enrollments in Northern Virginia have increased annually since 1974 when the Diocese of Arlington, once part of the Diocese of Richmond, was created. The Arlington Diocese covers all of Northern Virginia, stretching from Arlington south to Fredericksburg and Colonial Beach and west to Winchester and Woodstock.

The 33 Catholic schools in the diocese have 12,625 students, nearly a 20 percent increase over the 1974 enrollment, according to the Rev. William Davis, diocesan school superintendent. The system has added four schools and expanded four more --and parents are clamoring for more.

As the Catholic population in Northern Virginia increases--it's now estimated at about 180,000, or 10 percent of the area the diocese covers--the number of students attending parochial schools is increasing also.

But Catholic schools in Northern Virginia are gaining students at a time when public schools are losing them at a rate of about 3 percent annually and when Catholic school enrollments in Washington and the Maryland suburbs also are declining.

In Montgomery and Prince George's counties, where the Catholic population is higher than in Northern Virginia, Catholic schools have lost 10.7 percent of their students in the past five years while public schools have lost 23.9 percent. In Washington, Catholic schools have lost 3.5 percent and public schools 22 percent in those years.

In Northern Virginia, religious and lay people agree, enrollments probably would soar even more if the church could keep pace with the growing demand.

The principal attractions of parochial schools seem to be their teaching of religious and moral values, their traditional academic approach and their discipline.

"Teaching religion--that's what we're in business for," said Father Davis, the diocesan superintendent. "I think people are saying, 'We need that.' People are looking at the world we live in and are saying, 'Do I want my children to grow up in a world without something other than material desires?' They need something else to help them in the world today."

Ten to 15 years ago, Catholic schools across the nation were closing because of declining enrollments and the loss of teaching priests, brothers and sisters whose vows of poverty kept down school operating costs.

"I think the church went through a period of time when people sort of said Catholic schools weren't important," Davis said. "But we're turning around and people are beginning to come back as they realize we're giving them something they want. . . .

"I think we went through a phase where we were almost apologizing for being Catholic. We wanted to be good public schools, in a sense. . . . But I think the critical issue now is we're telling our people that we're proud of the fact we're Catholic. We do not want to be just carbon copies of good public schools. We want to be Catholic schools."

Of the 600 teachers in the diocese, only 24 percent are priests, sisters or brothers; nearly 10 percent of the lay teachers are non-Catholic. Almost 12 percent of the students are non-Catholic.

School principals, teachers and Davis all are reluctant to criticize public schools, which cannot screen applicants and must follow many federal and state regulations. But parents are not so hesitant.

Disenchantment with public school systems and what parents see as a breakdown in academic and disciplinary standards have prompted many parents nationwide to scrimp and save so their children can attend parochial or private schools.

Margaret Straight is one parent who is disappointed in public schools. A Methodist married to a Mormon, Straight has two daughters at Aquinas School, where about 20 of the 610 students are non-Catholic. Public schools, Straight said of her experiences, were "more interested in socialization than in teaching anything."

At Aquinas, Straight said, "The whole atmosphere is pro-learning, letting children grow in a disciplined setting, in contrast to public school, where peer pressure makes the kids want to be part of the gang, to get by, not excel academically."

Acknowledging that she "had some questions" initially about whether her non-Catholic daughters would "fit in," Straight said that school administrators, teachers and other students eased the way.

Like all students at Catholic schools in the diocese, non-Catholic youth must take the religion courses that are part of the curriculum. Straight said the religious training at Aquinas "is another way to learn to look at things, . . . to find your own set of values."

Nancy Knauf, who is Catholic, kept her children in a Baptist school until Aquinas opened as a regional school serving three parishes, including hers. "I don't believe in public schools," Knauf said, adding she is impressed with how respectful Aquinas students are of adults.

It cost about $13 million in 1980 to operate the 33 schools in the diocese. Tuition, the primary source of income, ranges from $150 to $670 at the grade-school level and from $1,225 to $1,670 at the secondary level. Each school, however, has a "family-rate" fee schedule that lowers the cost as additional children are enrolled. Parishes also subsidize tuitions at some schools.

"Parents may be rearranging their priorities," said Sister Margaret Mary, vice principal for academic affairs at Biship O'Connell. "Instead of buying another car or building a swimming pool, they're sending their children here.

"They're looking for religious values which have become increasingly important to them, and they're looking for good academic preparation. And they appreciate our discipline code."

Sister Christine, the principal at Aquinas, estimates that 60 to 70 percent of the families with children at the school have two working parents; often one is working solely to ensure that the children can attend parochial school.

The school sometimes draws its teachers from these ranks of parents seeking supplementary incomes, particularly wives of military personnel stationed at nearby Fort Belvoir or the Quantico Marine Base.

Of Aquinas' 20 teachers, 18 are lay staff, and Sister Christine said she is careful to emphasize that their salaries should be considered supplementary, insufficient to raise a family on.

Minimum starting salaries at diocesan schools are $8,250 for elementary teachers and $10,000 for secondary teachers.

Cheryl Lorson and Catherine Puttre, who teach 8th and 6th grades, respectively, at Aquinas, would be earning considerably more if they taught in public schools, where starting salaries for first-year teachers range from $13,711 to $14,224. But Lorson, who has taught public school in Virginia Beach, and Puttre, who taught parochial school in Brooklyn, said other benefits outweigh higher salaries.

Both pointed to the close working relationship the school staff has with parents and the high academic and personal goals the parents have for their children.

"The children know the sacrifices their parents are putting forth," said Lorson. "We're not an economically upper-crust area, so the children help out with paper routes and so forth, and it makes them appreciate what their parents are doing for them."

"Nobody's here for the money," added Puttre. "You're here because there is a sense of values here."

Richard J. Martin, assistant principal for student affairs at Bishop O'Connell, said, "It's tough to get good teachers, given the economic situation, to come into parochial schools. There has to be a certain amount of dedication, sacrifice. You have to weigh the financial compensations versus the ability to actually teach in an environment which is conducive to learning."

As at all parochial schools, Bishop O'Connell has a strict behavior code that transcends policies of requiring school uniforms, ties and jackets. None of the diocesan schools use corporal punishment, but there are penalties ranging from additional homework and restrictions during the school day for truancy and smoking to automatic expulsion for such things as using drugs or alcohol on school grounds.

"Some people think our job is easier because Catholic schools have leverage in that they don't tolerate obnoxious or uncordial behavior," Martin said. "(They think) if it becomes too bad, you can always make them leave. But you have to work at making it work. You have to talk to kids, counsel them as well as discuss things with them. Work to correct their behavior."

The discipline carries over into the classrooms, which predominantly fall into the "traditional" mode of classroom settings: desks neatly lined up in rows, books carefully tucked inside or under desks. Students stand when a priest or nun enters the room.

But the parochial school system is "far more open to individual approaches" today than in the past, said Father Davis. "We tell teachers there are different ways to teach--as long as you can teach this, go ahead and do it. There are children in those classes who learn in different ways.

"And while there are still things we think the children should learn, we try to get them to learn the best way we can. We're going 'forward to basics.' I don't want to go back and do something just because we did it that way years ago. . . .

"You can go into 10 different classrooms and see 10 different things. You might see learning centers, you might see them (students) at desks in order and a lot of other things. There's the freedom to do that now."

Classroom sizes generally parallel those in public schools: a maximum of 30 pupils per teacher, although the number is much lower in some classes.

And, like the public schools, parochial schools are finding their minority enrollments increasing. In the Arlington diocesan schools, 15 percent of the students are members of minority groups, up 2 percent from last year. They include about 1,100 Hispanic children, 360 Asians and 400 blacks.

Although they adhere to state standards on school and teacher accreditation by choice, Catholic schools get no financial aid from the state. The only federal benefits they receive are milk subsidies, Title 4 (library) funds and the services of Title 1 teachers to assist children with reading problems.

But, as Bishop O'Connell Principal Alward V. Burch noted, "Most of our kids do not have reading problems."

"If we have children with chronic behavioral or learning problems, we refer them to the public schools," said Sister Christine of Aquinas School, which has no guidance counselors or school psychiatrist. "We're not equipped to help those children. So if they need that kind of help, it would be a disservice not to refer them."

Catholic schools also do not have classes for special education students or those whose knowledge of English is limited, as public schools do, because offering such services would be too expensive, teachers and principals agree.

At the entirely lay-staffed Queen of Apostles School in Fairfax County near Alexandria, students represent 29 foreign countries, according to Principal Marilyn Bradberry.

"There were maybe four to six children who came in not speaking English," Bradberry said. "I recommended the public schools because we don't have an ESOL (English for Speakers of Other Languages) program, but their parents insisted they come here.

"I have never turned anyone away, so the option was that they couldn't go on to the next grade if they didn't progress as they should have.

"Maybe we demand more of our students," Bradberry added. "(But) because of what children are exposed to in the world today, school is even more important now than it would have been 25 years ago."