The Reagan administration has stopped the federal government's main college student aid program in its tracks while it seeks congressional approval of a plan to make low-income families pay a greater share of educational costs. o

Officials said yesterday that they had held up replies to tens of thousands of students who have applied for aid.

The administration tactic has put opponents of its proposed new aid formula in an awkward position. The Democratic-controlled House might be able to muster the votes for a resolution disapproving the change, but that could take weeks and leave large numbers of college students uncertain about the amount of federal aid they will get come next fall.

Thousands of applications for a 1981-1982 basic educational opportunity grant, the bedrock college aid program for children for the needy, have been put "on hold" at Systems Development Corp. in Santa Monica, the computer software firm with the contract to process them.

About 6 million students are expected to apply for the grants, which pay up to $1,750 of annual educational costs. Some 2.8 million students, about one out of four attending college or university, are getting the federal help this year.

The problem that has stalled the process is an attempt by the new administration to alter a Carter-era formula for determining how much low-income families should pay toward their children's college education.

Eligibility is based on net income -- total family income minus certain allowable living costs. Under a Carter regulation announced in January, the amount these families could deduct for their living costs in 1981-1982 was to rise by 12 1/2 percent to cover inflation. This would have reduced the amount the low-income familiy would have left over to meet college expenses.

But several weeks ago, the Department of Education announced a new regulation that would eliminate the inflation escalator. On paper this would leave the family with more disposable income to contribute to college under the program's formula.

Although President Reagan's administration claims this will save the federal government only $183 million in its 1982 budget, a congressional source predicted that the formula change could eliminate grants for several hundred thousand low-income students.

Under existing education law, Congress has 45 days to object to new regulations. A resolution from either chamber can prevent the rules from becoming effective.

Congressional sources said yesterday they hoped to avoid a time-consuming showdown by getting the Department of Education to substitute for the regulation now pending an across-the-board cut in the grants.

Department officials insisted yesterday that their plan would not affect the neediest families. And a number of higher education groups have praised the Reagan administration for leaving the Basic Educational Opportunity Grants program essentially intact.

The administration is seeking a supplemental appropriation to increase the maximum allowable award for fiscal 1981 and it has also announced it will increase funding in 1982 of another loan program, National Direct Student Loans.

However, the administration has acknowledged that the new criteria it is seeking could knock at least 100,000 students off the rolls of grant recipients. These students tend to be from families whose incomes range from $21,000 to $25,000 and whose access to bank credit to meet education costs is limited. Many of these families already are receiving aid from all other available federal programs.

In addition to the controversy over the grant problem, bankers also have expressed concern about Reagan proposals for tightening eligibility for federally subsidized loans to college students.

Some 2 million students, or one out of five, now get these loans under a program liberalized in 1978 to make all students eligible regardless of income. But under a Reagan plan requiring congressional approval, students will be eligible for the loans only if they still have unmet educational costs after their parents have contributed the full amount required under a formula.

The way the system now works, banks that make the loans can collect interest from the federal government quarterly as long as the student remains at college.

Reagan wants to make students pay 9 percent interest while they are at college, with banks collecting the money.Representatives of some local banks have said the costs and overhead might discourage them from participating.

Applications for loans for the 1981-1982 academic year usually start coming in April and May, which this year would coincide with the middle of congressional consideration of proposed changes in the law.

"Some of the banks have been frightened but we plan to play by the same rules until we're told differently," said Benjamin LeBorys, an official of Union Trust in Baltimore, which made some 3,500 loans in the last seven months.