The District of Columbia may be experiencing the greatest outbreak of Hong Kong flu among children since 1957, according to officials at Children's Hospital National Medical Center.

Officials in Maryland also report outbreaks of influenza and increased absenteeism in various schools in Anne Arundel, Baltimore, Carroll, Frederick and St. Mary's Countries and in Baltimore City.

In Virginia, several schools have reported low attendance because of flu-like illness but no confirmed cases of either A/Victoria or B/Hong Kong flu have turned up, according to a state health officials.

The symptons of the influenza and flu-like illness include muscular aches, high fever, coughing and sore throats. The illness typically last about two days.

Children's Hospital reported yesterday that it has been "swamped" with patients. The hospital's outpatient clinic and emergency room normally see about 140 to 160 patients a day, but on Monday 274 sick children came in to the hospital according to public relations director, Harold Kranz Jr.

Dr. Robert Parrott, director of Children's said that the number of cases of B/Hong Kong seen in the hospital in the last three weeks is higher than at any time since 1975. B/Hong Kong is a type of flu that is common in the winter.

Parrott qualified that estimate, however, by noting that Children's is sampling more patients with flu-like illnesses at the request of the National Institutes of Health. As a result, Parrott said, the increase may reflect the larger sample being taken rather than an actual increase in B/Hong Kong over previous years.

"When we've seen this much before." Parrott said, "there's been a community outbreak or epidemic, whatever yo want to call it."

Dr. Martin Levy, chief of the communicable diseases control branch of the District has a "Sporadic outbreak," with two public elementary and one parochial school reporting high incidences of flu-like illnesses, but no unusual outbreak among adults.

Parrott said he knewof no cases where a patient had died of B/Hong Kong influenza, although in 12 of 22 confirmed cases patients had to be hospitalized. Another 30 cases of suspected B/Hong Kong flu still are awaiting confirmation.

The 52 suspected and confirmed cases of B/Hong kong at Children's represent only random sampling of all the cases seen at Children's.

In Fairfax County, Dr. John Einarson, the assistant director of the county health department, said a "flu-like virus" has been reported in several county schools. Health and school officials did not have statistics on the number of students affected by the flu.

At Churchill Elementary School in Mclean, a school official said 15 students were sent home from school yesterday because they were suffering from symptoms of the flu. School attendance had been low - with 90 students out of 400 absent on Monday and 70 students out of classes yesterday, according to the Churchill counties and Alexandria said they are not experiencing an unusual number of school ahsences as a result of the flu.