The violence took place in three universities in or near the capital, Dhaka, as well as in the southern city of Chittagong and Kushtia in the west.
At least 100 students have been injured in the clashes, which the authorities say have taken place only on campuses.
A military-backed government has run Bangladesh for the past six months.
Many of the demonstrators called for the country to return to democracy, which the government has promised to restore by the end of next year.
At the worst clashes at Dhaka University, students threw stones and set fires across the campus. Police responded by using batons and tear gas. At least 15 students were injured on Tuesday in the second day of clashes.
The students have set a Wednesday deadline for an army camp at Dhaka University to be disbanded.
They burnt an effigy of the army chief, Moeen U Ahmed and tried to assault the vice chancellor, police said.
Dozens of vehicle were set on fire, including an army jeep.
The BBC's Waliur Rahman in Dhaka says that two other military governments in the past - that of Ziaur Rahman and Muhammad Ershad - were both brought down in protests that were started by students.
The army is reported to be keeping a low profile in the clashes, leaving the job of confronting the students to the police.
But the government has said that action will be taken against troublemakers, who if necessary will be removed from campuses.
It has vowed to stamp out corruption before the country returns to democracy, but discontent has been rising in recent months.
The current trouble was sparked by an argument between a group of students and members of an army unit that has been garrisoned at Dhaka University since January.
Last Mod: 21 Ağustos 2007, 23:44
It quickly degenerated into a full-scale riot - in defiance of the emergency laws against gatherings and protests.
The students told the BBC that they wanted the army to leave the university and withdraw from politics.