A second round will be held on June 18. Of the council's 264 seats, 132 are renewed every three years.
Amendments
Of the 665 candidates in the running, 88 are elected and 44 are appointed directly by Hosni Mubarak, the president, who has ruled Egypt for more than a quarter of a century.
The council has a consultative role.
Egypt's constitution, which is partly based on the Sharia (Islamic law), was amended in March to ban any political activity based on religion.
But the amendments did not deter the Muslim Brotherhood which is fielding candidates as independents.
The group, which is officially banned, gained 88 seats in the 2005 legislative elections, to control one fifth of parliament.
Freedom of expression
Safwat al-Sherif, speaker of the Shura Council, has warned the Muslim Brotherhood that it was ready to crack down on groups that "defy the constitution and the law".
Egyptian authorities have arrested 22 supporters of the Muslim Brotherhood candidates in five provinces, Al Jazeera's correspondent in Cairo reported on Sunday.
The run-up to the elections has been marked by mass arrests of members of the Islamist group accross the country, including two on Saturday, bringing the number of members arrested to 126 in one week, a security source said.
Mohammed Habib, the group's deputy supreme guide, said on Friday on the group's website that 668 members are currently detained.
Forty members face a military trial on charges of money-laundering and financing a banned organisation.
The human rights group Amnesty International described the wave of arrests as a "serious violation" of freedom of expression.