Israeli shells have fallen on Beirut's only synagogue, sending dozens of Jewish families fleeing for safety, residents said today.

Before the Israelis invaded Lebanon to crush the Palestine Liberation Organization, about 100 Jewish families lived in the quarter near the Maghen Abraham synagogue on Wadi Abu Jamil Street in the northern half of Israeli-ringed west Beirut. It is a few blocks from the so-called green line that divides the capital into Moslem and Christian sectors.

Now the once-lively neighborhood is virtually abandoned. Seven Jewish families remain, members of the community said in interviews. No Harassment by Arabs

''My house is broken, my house is broken,'' an old Jewish woman, practically deaf, mumbled in French as she sat in a chair behind the synagogue.

Jewish residents say they have not been harassed by their Moslem neighbors or the Palestinians since the Israelis invaded Lebanon on June 6.

Neighborhood residents, including the Jewish families, said Israeli artillery firing from east Beirut and gunboats cruising offshore had persistently pounded the district, which is also populated by large numbers of Kurds and Lebanese Shiite Moslems.

A week ago, during a fierce Israeli assault, a shell blew a hole in the roof of the cream-colored stucco synagogue, sending about 60 Jewish and Moslem refugees sleeping there fleeing into the street, residents said. The building is now locked and vacant, plaster and concrete strewn on the floor. Without Water for a Week

A block away, 80-year-old Khuder Namoud lives on the fourth floor of an apartment building with his wife, Rachel, and son and daughter, Ibrahim and Lisa. Their apartment has been without water and electricity for a week, Mr. Namoud said.

''We are sick of this war,'' Mr. Nahmoud said, his son interpreting from Arabic. ''All the money is gone. We can't work. The electricity is gone, the water too. We have just stayed here in the house for two months.''

Wearing a Jewish prayer shawl and skullcap, he said he prays daily for the bombardments to stop. His son said about seven families remain - the ones without enough money to flee. The others have gone to Junieh, the Christian port north of Beirut in an Israeli-held area, or to safer districts in east Beirut, he said. Israel has said several families have emigrated to Israel since the invasion.