The phones started ringing in the career center at Mount Vernon High in Alexandria on the first day of school. The Northern Virginia Park Authority had nine openings. Giant was looking for grocery baggers to work Saturdays.

Nancy Van Metre, school career coordinator, realized there could be only one group more disgruntled about the start of school than youngsters: local employers battling a labor shortage in low-skill and entry-level jobs.

"Anybody who had college kids for the summer has a problem," she said as dozens of jobs listings piled up.

So desperate are employers in the Washington area right now that many have made special appeals to students to stay on the job past the traditional end of summer, Labor Day. They're offering split shifts, higher wages and looking for workers in schools, at the checkout counter and through a record number of ads in the newspaper.

The loss of student help comes at a time, employers say, when the labor shortage in the area appears to be intensifying. Job growth in the Washington area has outpaced the national average during the past few years and unemployment has continued to sink to surprising lows.

"For the first time, this summer we had twice as many jobs as students. And the problem is just getting worse," said Walter Wolfe, employment training coordinator for the Montgomery County Department of Family Resources.

Youth unemployment nationwide has dropped dramatically during the past five years, according to the Labor Department's Bureau of Labor Statistics. In July 1983, 16.2 percent of workers 16 to 24 years old who wanted jobs couldn't find them. This year, that rate dropped to 11.7 percent.

Job program counselors in the Washington area scrambled throughout the month of June to match thousands of students with businesses in need of clerical workers, typists and retail clerks. Today, of the 24,000 students who received jobs created through the District's youth program, 2,000 are staying on with their businesses this fall, according to city officials. In the suburbs, where employment offices received fewer applications, state job program coordinators such as Wes Caison of the Virginia Job Service found "a lot better-paying jobs were available to youngsters this summer."

"I think it's fair to say that all the young people who want to continue to work {during the school year} can still work," said Caison, office manager in Falls Church, largest of four employment offices in Northern Virginia. "We're seeing restaurants that are using job applications as placemats and advertising tuition programs to students on the plastic dividers that usually promote the dessert of the day."

A partial explanation for the scramble can be found in the latest unemployment figures. Even the District, where joblessness has held steady at 7 percent despite a 3 percent rate in the suburbs, is beginning to feel the pinch for employes. For the first time in six years, unemployment in the District fell in the summer. The jobless rate in July was 6.2 percent, the lowest in more than 15 years; at the same time, the suburban rate dropped slightly, to 2.8.

A good barometer of the need, newspaper classified ads, is just another testament to the problem facing many employers. Today's Washington Post carries 78 pages of classified employment ads, a record number for this time of year and nearly 12 percent more than last year.

"It's been harder to see workers go this fall because the regular job market is so tight," said Evelyn Kenley, personnel representative for Giant Food stores. During the summer, 200 to 300 students were hired at stores in Montgomery and Fairfax counties to stock produce and bag groceries, she said. With the start of school, she said, some Giant stores "are doing everything we can to keep them on."

"We're trying to fit the student hours as much as we can," she said. "At our gourmet store in Rockville, we're offering Saturday-only jobs."

The labor pinch appears to know no boundaries. Both large and small businesses are having problems attracting the young. Whether inside or outside the Capital Beltway, some business owners are clamoring for help from their communities to fill in the gap.

In Montgomery County, the Economic Development Council is forming a task force of small business owners to look at problems with hiring. Several malls in the area, including Lakeforest and Montgomery, recently sponsored job fairs that attracted few youths. It is time, according to Ben King, owner of Gaylord's Lamps and Shade and a member of the task force, to address what they see as a crisis.

"We've had to close on Mondays because of the lack of workers, and we've had to cancel sales," King said. "The schools have been fairly good sources for labor, but once school starts, it just makes a bad situation worse . . . . What we need to do is put together a network of job resources."

At Peoples Drug Store, a chain with 170 stores in the metropolitan area, individual store managers are getting help from their corporation to attract stock clerks and cashiers. The company is supplying them with mini-application forms to stuff in customers' bags at the checkout line. This month, the company finished filming of a slide show that will be taken on the road and shown at local high schools in hopes of drumming up a few applicants.

"The unemployment picture is certainly tight," said Mark Arensmeyer, vice president for personnel. "We all know the demographics. Now we're just trying any way to get the workers we can."