Lukashenka also used a referendum in 1996 to extend his stay in power. Western observers considered that vote to be a fraud, but the extension means that the next presidential election is not until 2006.
To change the constitution, today's referendum must have the support of more than 50 percent of the country's 7 million eligible voters. But a Gallup Organization/Baltic Surveys poll of more than 1,000 Belarusians earlier this month found that only 41.5 percent said they'd vote for the change.
The Organization for Security and Cooperation in Europe (OSCE) and other monitoring groups have sent hundreds of observers to Belarus. Opposition parties have warned that they expect widespread vote rigging.
After voting in Minsk today, Lukshenka, told journalists to stop worrying so much about the issue of electoral fraud: "For 10 years I have been working and for 10 years you [Western journalists] have been expressing concern about something in Belarus," he said. "I think it is about time for you to relax and to stop reproaching us about some sort of falsifications or violations."
On 15 October, U.S. State Department spokesman Richard Boucher said there are already indications that the poll will not be free and fair. "The U.S. and the European Union have repeatedly called on Belarusian authorities to abide by international standards in conducting elections and referenda. Unfortunately, Belarusian authorities have not upheld their commitments in the conduct of past referenda and elections and according to the reports of the Organization of Security and Cooperation in Europe, the current campaign has been marred with irregularities."
Voters are also deciding who will sit in Belarus's 110-seat parliament. Parties opposed to Lukashenka are only expected to win a small number of seats, although most political power rests with the president.
Belarus's Central Election Commission has been busy removing opposition candidates from the ballot for various reasons. One was removed on 15 October for allegedly slandering the president.
A voter in Minsk, computer programmer Mikhail Rubin, said two opposition candidates he planned to vote for were knocked off the ballot. "I voted against the referendum. Unfortunately, on the parliament vote they threw out [opposition] candidates Senkevich and Volchik so I voted for [opposition candidate] Vladimir Kolos; I think the constitution is something that we shouldn't touch," Rubin said.
At the same polling station, state social worker Natalya Golikova, threw her support behind President Lukahsenka and the change to the constitution. "I voted, of course, for the referendum. It is only my personal opinion. I support our head of state and I like his politics," she said. "I like living in our state. I trust Alyaksandr Lukashenka."
Under Lukashenka's rule, independent media and opposition groups have faced official harassment. The president has also been accused of involvement with the disappearance of four opposition figures.
Despite the intimidating atmosphere for those in the opposition, a few young people defied a ban on official rallies and showed up in the center of Minsk Saturday wearing black ribbons and silently protest against Lukashenka's rule. One of the demonstrators was Dmitry Tsarevich.
"It does not matter that there are not many of us here," he said. "Only a few people protested during the communist era and they were imprisoned -- but the system crashed anyway. This system is much weaker and if our fathers managed to knock down communism, we will knock down this one."
The government of Belarus has used its control of the media for a heavy advertising campaign in favor of changing the constitution. Voters are being told that life has improved under Lukashenka. However, the average salary in Belarus is still only about $150 a month.