Alya Lutfi, who works as an accountant and who was waiting outside the polling station, said it seemed as if "there is no election today".
The elections concern only half of the 264 seats in Egypt's Shura Council and of that, only 88 seats are elected, with the remaining 44 appointed by Hosni Mubarak, the president.
Previous Shura Council elections have witnessed low voter turnout, a reflection of widespread apathy towards the 264-seat consultative body and Monday's elections got off to a slow start.
Amr el-Kahky, Al Jazeera's Egypt correspondent, said: "The turn out this morning is very low as expected. Usually the Shura elections, the upper house, is not that important to people."
He said: "People say they are not that much interested as they have their own problems such as earning a living."
The constitutional amendments give greater powers to the upper house but impose wider restrictions on the Muslim Brotherhood, the ruling National Democratic party's main challenger.
The elections are also a test of a new law banning the use of religious symbols and slogans, a move seen as an attempt to drive Islamist groups, such as the Muslim Brotherhood, out of mainstream politics.
However, on the eve of voting, an Egyptian court denied a request by the electoral commission to disqualify eight of the Muslim Brotherhood's 19 candidates from standing.
Members of the National Democratic party had petitioned the commission to eliminate the Brotherhood candidates, alleging they had broken the law by campaigning under religious slogans.
But the Supreme Administrative Court ruled on Sunday that there was no conclusive evidence that the candidates or their supporters had used religious slogans.
Candidates other than the Brotherhood have used Quranic verses on their election posters and many of the National Democratic party candidates have chosen as their election symbol the crescent moon, which has religious connotations.
During preparations for the elections, the police intensified a crackdown on the Brotherhood, which says that more than 760 of its members are now in detention, 600 of them picked up since the beginning of the campaign last month.
The Egyptian government outlawed the Brotherhood in the 1950s but has allowed it to operate under tight restrictions.
Despite the constraints, however, members from the group ran as independent candidates in the lower house elections of 2005, winning about one-fifth of the seats in parliament and confirming the Brotherhood's position as the country's strongest opposition movement.