Elementary school enrollment in Prince William County rose from 15,334 students in 1983 to 15,598 this year.

The upward trend is projected to continue at a steady pace, according to school spokeswoman Kristy Larson. Larson said an increasing birth rate and an increase in residential development, especially in the eastern end of the county, contributed to the higher enrollment. The school system lost 400 students in 1982.

A recent student housing report said that while high school and middle school enrollments will show some increases in the next three to five years, elementary school enrollments are projected to rise "significantly." Projected elementary enrollment figures for 1986 show an increase of nearly 800 students more than this year, the report said.

The major problem school administrators face within the next two years is overcrowding at nine of the county's 31 elementary schools. They are: Lake Ridge, Dumfries, Enterprise, Coles, Elizabeth Vaughn, Kilby, Occoquan, Minnieville and Sinclair. According to the report, Dumfries Elementary already exceeds its capacity by approximately 126 students. The report recommended that at least two of the five portable classrooms now being used at Dumfries remain.

Some relief from overcrowding in the eastern end of the county is anticipated with the scheduled September 1985 opening of Springwood School on Springwood Drive and Alexander Henderson School on Cardinal Drive, each with a 700-student capacity. The report has also recommended boundary changes once the new schools are operating, to relieve overcrowding in the older facilities.

Larsen said that overcrowding was expected to remain a problem for three to five years, due to a projected increase in new housing starts and a "baby boomlet."

A third factor the report cited to explain the rise in enrollment and the projected growth was that the number of students attending private or parochial schools in the county was 5.5 percent, half the national average.