Prince George's County education officials are bracing for a severe fiscal crisis that could force them to slash hundreds of teaching and administrative positions from next year's budget and to consider closing a dozen or more public schools over the next three years.

Preliminary budget estimates presented to the school board at a closed session earlier this week showed that the system will have in effect an $18 million revenue loss next year because of the county's tax-limiting TRIM amendment, high inflation and the loss of some federal aid.

The work-force cuts and school closings were offered to the board as options that would allow the system to adjust to the large revenue loss, which officials said would make it impossible for the county to maintain its current level of school programs.

Prince George's is the only jurisdiction in the Washington area where voters similar to California's Proposition 13. The property taxes are the single largest source of funds for the county's school system.

This year, the first under the TRIM mandate, county and school officials were forced to adopt a number of controversial cost-cutting measures, including school closings, reduced park services and classroom teacher reductions. In the county government and in the schools, officials are predicting that next year will be far worse.

"I don't think we were prepared for the magnitude of the problem," said school board vice chairman JoAnn T. Bell. "If this continues, we'll be put in the position of funding only mandated programs -- simply the reading, writing and math, and none of the other exposures."

According to George Ridler, budget director for the schools, preliminary estimates for next year show expenditures of $274.3 million, but the projected revenues are only $256.3 million.

The shortfall is caused by an expected reduction of $5 million in federal impact aid to the school system (aid designed to compensate for added enrollments caused by the presence of federal institutions) and by the inability, because of TRIM, of the county government to give the schools any more money to deal with rising costs.

The schools received $155.8 million from the county this year and will ask for $159.4 million next year, an increase that does not even cover inflation, Ridler said. Ridler noted that the teachers' contract provides for a 7 percent cost of living increase next year, which will cost the schools about $10 million more in salaries.

County executive Lawrence J. Hogan said yesterday it was "highly unlikely" that the schools would get as much money from the county as they are requesting. "We have the pressure from all over the county government, where prices are going up all over and our resources [because of TRIM] are staying the same. There will be cuts everywhere," he said.

To make up the shortfall, the school administration is considering a pool of about 60 elementary and junior high schools for closing in 1981 or 1982, sources said.

School officials declined to comment on the possibility of closings or to identify the 60 or so schools.

The administration has also proposed the elimination of about 200 teaching positions and 59 administrative posts in the system's area offices. many of those positions will be reduced through attrition, school sources said.

An assistant superintendent who is retiring this year will also not be replaced, sources said.

"Right now, we're taking a good hard look at the figures and trying to face the possibility that this [the $18 million shortfall] may happen," Ridler said.

School Superintended Edward J. Feeney will submit his recommended budget to the school board members for their consideration around Dec. 1. The school board will then consider his recommendations, make any changes and submit the final budget to Hogan for consideration in March.