DHAKA, Bangladesh (AP) _ The roof of a university dormitory collapsed on about 500 students under torrential rain from a storm roaring inland from the Bay of Bengal. Hospital sources said today at least 71 people died and rescuers expected the toll to increase.

Newspapers reported that the death toll at Dhaka University could be more than 100, with many victims still buried beneath wreckage.

The storm came ashore from the Bay of Bengal this morning, lashing Bangladesh and southeastern India with winds of up to 93 mph. Dhaka is about 150 miles inland.

Thousands of people were evacuated from offshore islands and coastal areas as officials sought to avoid a catastrophe similar to the May 24-25 storm in which an estimated 11,000 people were killed. Most of the dead from that storm were lived on the coastal island of Urichar.

Hundreds of tons of girders and cement crashed down on about 500 Dhaka University students at about 9 p.m. Tuesday as they watched a popular television program inside a dormitory auditorium.

The building was undergoing repairs when the accident occurred. One student said the outer coating of the roof was removed earlier in the day.

''It is impossible to believe that authorities had allowed the use of the auditorium when it was in an abandoned condition,'' a senior civil engineer told the The Associated Press. He spoke on condition he not be identified.

Hospital sources said today that 71 students died in the tragedy. State-run Radio Bangladesh said at least 31 bodies had been recovered by this morning.

Monaranjan Dhar, a student involved in rescue operations, said more bodies are expected from the debris of the hostel's auditorium roof.

Rescue officials said at least 100 people were injured.

Two English-language newspapers, The New Nation and The Daily News, reported at least 100 people were feared dead and 300 injured in the roof collapse.

Army, fire brigade and police teams looking for survivors used cranes to remove debris at the three-story dormitory for men. But rescue workers were hampered by rain, lack of equipment and lack of power.

Muniruzzman Badal, president of university's student league, said many bodies were still buried.

Dhaka's three main civilian hospitals were packed with victims, brought in by ambulances or by fellow students carrying people on their backs because of a shortage of stretchers. Some of the most seriously injured were taken to a military hospital.

A doctor at Dhaka Medical College hospital said: ''It is horrible. We are confronted with a gigantic task.''

''There is an acute shortage of blood and medicine,'' said a doctor at the Post-Graduate Medicine Hospital. ''We need blood immediately to save many lives.''

The building served as the provincial legislature before the civil war that made East Pakistan the independent nation of Bangladesh early in 1971. It now is called the Jagannath Hostel and serves as a dormitory for minority Hindu, Buddhist and Christian students.

Government officials ordered three days of mourning for the victims. An announcement said flags would be flown at half staff and all educational institutions across the country would remain closed during the mourning period.

As the storm came ashore, Bangladesh state radio said the islands of Sudharam and Char Clark were under 6 feet of water. India's state-run television said waves of 6 to 8 feet were expected to flood low-lying areas. Fishermen were warned to stay in port.

Rescue teams were asked to stand by for emergency operations, and storm warnings were posted throughout the coastal area, officials said.