The polling is being held to elect 331 members of 22 zila parishads and 2,902 members of 146 panchayat samitis across rural Punjab.
At least 38,000 police personnel have been deployed at 19,350 polling booths, of which 2,650 are sensitive.
The elections are being held in 12,000 villages spread across the state. The counting of votes would be taken up on May 21.
In the run up to the polls, two persons died in a clash between SAD and Congress activists at Lopoke in Amritsar, one Congressman died at Patti and another at Bathinda district.
Opposition Congress has in a bid to take on the ruling SAD-BJP combine tied up with the People's Party of Punjab and the Left parties in some areas this year.
Last time, these polls were swept by SAD-BJP, which was in power, and the Congress won in 2003, when it was ruling Punjab.