Celebrations include all-night song and dance performances in the capital, Harare, and a speech by President Robert Mugabe in the city's stadium.
Mr Mugabe, who has ruled since 1980, leads a unity government with rival Morgan Tsvangirai as prime minister.
On the eve of the anniversary, a civil rights group said four of its members had been denied bail after they were accused of staging an illegal protest.
The group, Women of Zimbabwe Arise (Woza) deny wrongdoing. The four were part of a group of women demonstarting against regular power cuts and high electricity tariffs in Zimbabwe.
Economic woes
Zimbabwe declared independence on 18 April 1980, following a seven-year conflict against Rhodesia's white minority rule. Mr Mugabe, a former guerrilla leader, was elected president.
Independence also brought crippling international sanctions to an end.
The new country was widely seen as a new model for Africa.
Zimbabwe experienced strong growth in its first decade but the economy began to decline in the 1990s.
In 2000 Mr Mugabe launched a controversial land reform programme, seizing white-owned farms and handing them to blacks.
In the following years, farm production and the currency went into free fall. The one-time food exporter became dependent on aid.
Meanwhile Mr Mugabe suppressed the opposition, saying it was in league with former colonial power Britain.
In 2008, the opposition Movement for Democratic Change won a parliamentary majority. But MDC leader Morgan Tsvangirai withdrew from the presidential run-off, citing violence against supporters.
However the two sides reached a power-sharing deal later in the year.
New elections are due to be held but no date has been set.
Story from BBC NEWS
