Prince George's County School Superintendent Edward J. Feeney yesterday submitted a preliminary budget to the county school board that cuts 536 teaching and staff positions, eliminates summer school for elementary students and reduces the amount of money available for new books and other supplies.

Despite the cuts, which Feeney said were the result of the most severe cost-cutting measures ever, the proposed $287.6 million budget for next year is $9 million higher than the current budget.

The increase is primarily the result of inflation, higher fuel oil costs and nearly $10 million in annual wage increases, school officials said.

In his cover letter to the school board, Feeney said he made the stringent cuts to satisfy demands imposed by TRIM, the county's property tax curb. County property taxes are the school system's single largest source of income.

County Executive Lawrence Hogan has told school officials that he will increase the county's portion of their budget by no more than $6 million next year. But the proposed budget calls for an increase of $13 million in county funding.

Feeney told the board that without the necessary county funding, the school administration would be forced into "programmatic changes that would seriously affect the educational program."

This year, the first under the TRIM charter amendment, school officials were forced to adopt a number of controversial cost-cutting measures including school closings, elimination of junior high school interscholastic sports and a reduction in the number of classroom teachers.

The proposed budget does not call for school closings this year, but school officials have said that at least 10 to 15 elementary and junior high schools will have to be closed by 1981.

Among the staff reductions proposed in Feeney's budget are 356 teachers, administrators and counselors assigned specifically to schools. Those cuts will be made through attrition, and class sizes will not have to be increased because student enrollments are declining, school officials said. The budget cuts out all but one of the current 13 reading specialist positions in the system.

The budget also eliminates 55 system-wide administrative positions. Some of those people will be reassigned within the system, but many will have to look for jobs elsewhere, school officials said.

The budget proposes cutting 100 custodial staff members and 25 bus drivers and aides. The staff reductions are expected to save the school system nearly $9 million.

The money budgeted for new text books, other supplies and maintenance materials was $10,000 less than this year. School officials said, however, that translates into a much greater reduction because of the current high rate of inflation.

"There will probably be a lot more rebinding" of books, one official said.

In addition to eliminating summer school for elementary school students, school officials said that some reductions will be made in the number of secondary school students who are permitted to use the summer program.

School board members said yesterday tey had been prepared for the stringent cuts proposed in the superintendent's budget by a closed-door meeting they had earlier this year with the superintendent's staff.

At that meeting board members were warned that next year's budget would have to be slashed because of increased costs, a reduction in federal impact aid to the school system (aid designed to compensate for added enrollments caused by the presence of federal employes in the area) and the county's tight financial situation.

Board chairman Jo Ann T. Bell said yesterday, "We knew it was coming and I think we are trying to cope with a disastrous situation as best as we can.

"The last thing we want to touch is the programs going to youngsters," Bell said. "It obviously means that we'll have to make some of those hard decisions about extracurricular activities."

Last year, one of the board's most controversial cuts was the elimination of interscholastic sports at the junior high school level and replacing it with an intramural sports program that has not been very well attended.

The final decision on the school budget will be made by Hogan, along with the County Council.