Some 32 million Ethiopians - 90 per cent of eligible voters - are expected to vote at more than 43,000 polling stations across the country.
Al Jazeera's Andrew Simmons, reporting from the capital Addis Ababa, said most people were wondering by what margin the ruling Ethiopian People's Revolutionary Democratic Front (EPRDF) would win, rather than whether it would win.
The EPRDF's biggest challenge comes from the eight-party coalition Medrek - or the Forum - but it is united chiefly by its desire to unseat Meles and has not set out clear policies, our correspondent said.
The opposition admits that it has little chance of victory but says that is because the EPRDF has tightened its grip on power since the 2005 polls, routinely intimidates and jails its critics and tries to divide the opposition.
In 2005, riots broke out in the capital when the EPRDF was declared winner. Security forces killed 193 protesters and seven policemen also died in trouble that tarnished the reputation of one of the world's biggest aid recipients.
The EPRDF says it has since won popularity during a period of sustained economic growth by building roads, hydro-power dams and electrifying villages in a country where nearly 10 per cent of the population needed emergency food aid last year.
There were concerns over whether Sunday's vote would go peacefully, our correspondent said, and what would happen if there were again a dispute over the results, but he said that the political atmosphere was very different from five years ago, with people mindful of what happened in 2005.
While there has been some violence in the two regions of Oromia and Tigray, the capital has been calm before polling.
Outside the capital, both sides say activists have died in politically motivated killings.
Diplomats and staff of some foreign charities have been banned from leaving Addis Ababa without permission from the authorities until after the poll.
In Tigray, the ruling party is facing a challenge from former members who fought with Meles over economic policy and how to deal with rival Eritrea.
Meles became leader of Ethiopia in 1991 when an armed group led by him ousted a communist government that killed hundreds of thousands of Ethiopians in a 17-year rule.
He was lionised by the West in 1991, with the then US president, Bill Clinton, calling him one of a "new generation" of leaders who would bring democracy to the continent.
But Meles, 55, has increasingly been criticised by rights groups, who say he is becoming more autocratic and stifles dissent in the country of 80 million people.
Birtukan Mideksa, leader of one of the Medrek member parties and seen by analysts as a potential replacement for Meles, is in prison accused of violating the terms of a pardon that released her from a previous jail spell in 2007.
Medrek is running 421 candidates for the 547-seat federal parliament, not as high as the EPRDF's 521, but enough to form a clear majority should they pull off a shock win.
The next biggest opposition parties, the All Ethiopian Unity Organisation and the Ethiopian Democratic Party are running 350 and 250 candidates respectively.