The election, with 4,000 candidates representing 39 parties and coalitions, is the seventh since the fall of communism in the 1990s.
Since the fall of communism, all elections in Albania have been disputed and marred by violence.
The Balkans state has joined the Nato military alliance and took its first small step towards joining the European Union by submitting its membership application in April.
The EU has indicated that any progress towards membership for the predominantly Muslim nation of 3.6 million that remains one of Europe's poorest countries depends on holding peaceful elections that meet international standards.
Some 3,000 monitors - including 500 foreigners - are to observe the voting process.
At the final rally in Tirana, the capital, late on Friday, Berisha called on "all Albanians to be united behind our European dream, to unite in our effort to make Albania similar to the whole of Europe".
Addressing a separate rally, his opponent Rama, the mayor of Tirana, said the "time for a big change is about to come".
"The Socialists are those who will take Albanians towards Europe, for the Democrats have lost their chance," Rama said.