They have called for an open debate to allow women to drive 'in accordance with religious and social norms', Gulf News reports.
Under the by-laws, the Shura Council has to respond to all questions, queries and petition.
According to Saudi news site Sabq, Sulaiman Al Zayadi, the former head of the rights and petition committee that submitted the petition and requested a date to debate on the issue, said debating the issue of allowing women to drive gives the Council greater credibility.
He added that if women were given the right to drive it will promote trust among the people who will view the Council as their representatives who are ready to engage in the debates they suggest.
The petition was handed before the end of the last session to the committee that approved it and suggested its debate by the Shura Council members.
The study argued that local social and economic developments in Saudi Arabia and the international covenants endorsed by the Saudi kingdom require that Riyadh allow women to drive cars.
According to the report, the study said that an advisory and executive committee should be set up by Saudi Arabia to draw the religious, social and security regulations to allow women to drive as a prelude for social changes that will make the society more recipient to the idea of women driving.