The vote being staged over six weeks is Egypt's first free polls.
The army, which took over after Mubarak was ousted, remains in charge until a presidential election in mid-2012, but parliament will have a popular mandate that the military will find difficult to ignore as it oversees the transition.
The ruling army council fuelled suspicions it wanted to hang on to power, even after a new president was elected, when its cabinet proposed inserting articles in the new constitution that would have shielded it from civilian scrutiny.
Parliament's prime job will be appointing a 100-strong assembly to write a new constitution which will define the president's powers and parliament's clout in the new Egypt.
