At daybreak yesterday the Mohammed Shouk family of Bowie began dressing carefully in their finest clothing from their native Iraq.

They had been up all night, praying and reading from the Koran, the holy book of Islam. For the last month they had fasted every day from sunrise to sunset. Now they were ready to welcome Id Al Fitr, the holiest day of the Islamic year -- the conclusion of the holy month of Ramadan.

Mrs. Shouk dressed the two girls in their new long dresses with pink flowers and bows. The boys wore new suits, ties and shoes. Mrs. Shouk wore a floor-length caftan of reddish brown with a heavy white scarf about her head and shoulders.

Then they made their way to the Islamic Center in Northwest Washington where they joined hundreds of Washington area Moslems who had gathered to pray and celebrate.

Id Al Fitr is a sort of Easter of Islam, the festival of the breaking of the fast following a month of self-denial and atonement.

As a reward for thie Ramadan fast, Moslems in many countries feast on rich foods and exchange gifts for three days afterward.

In some countries, a Christmas-like atmosphere reigns as well, with children basking in the money and gifts they receive from relatives.

Once the Shouks arrived at the Islamic Center, 2551 Massachusetts Av. NW, they separated, in the Islamic tradition. Mrs. Shouk and the three youngest children proceeded to a huge canvas and clear plastic tent where other women and young children sat. Shouk and his 9-year-old son entered the mosque where 1,500 other men and young boys were cramed.

As the hundreds of worshipers turned into thousands by 10 a.m., the air became stifling in the mosque, three tents and community rooms where people sat elbow to elbow on prayer rugs and sheets, awaiting the congregational prayer service. Mountains of shoes stood outside the entrances of all the rooms, as shoes may not be worn in a mosque or Moslem place of worship. Loudspeakers broadcast the Arabic prayers, sung in a near monotone.

Like a wave, the hushed crowds stood. Most of the women hurriedly covered themselves with their shawls, scarfs and headdresses as required by Islamic law.

With the final prayers, the worshipers hugged, kissed and greeted those surrounding them and the solemnity quickly changed to a festival atmosphere.

Within 15 minutes the crowd dwindled to 1,000 as the faithful hurried home to enjoy family celebrations and feast on rich foods eaten only on holidays.

"I feel so good." said Waduda Jami, spinning gleefully. "I completed my fast and now I know all my sins are forgiven. I can feel the difference." Jami, 30, an American black Moslem, came with her two children to the mosque. Her husband took off several hours from his job as a D.C. cabdriver, and returned to work immediately after the prayer service.

Jami held out two round flat pieces of yellow Play-doh which her 3- and 4-year-old children had given to her as holiday gifts "they made themselves."

"Most non-Moslems look on this as a hardship," said Jami. "But you look forward to Ramadan as a chance to make up for your sins."