Electors in the four constituencies could be seen reaching polling stations even before voting started at 7 a.m.
"There has been no report of any delay in starting the poll process," an election officer told here.
The main contest is between the Congress and the Akali Dal-BJP alliance.
Besides, the AAP, the BSP and the Lok Insaaf Party have also fielded their candidates.
Nearly 7.68 lakh voters in all four assembly segments will decide the fate of 33 candidates.
The by-election to Jalalabad seat was necessitated because of former Deputy Chief Minister and Akali Dal President Sukhbir Singh Badal quitting the seat.
Dhaka seat was vacated by AAP's H.S. Phoolka and Phagwara by BJP's Som Parkash.
Mukerian is going to polls as sitting MLA Rajnish Babbi of the Congress passed away.
The Congress has fielded former state youth Congress chief Raminder Awla from Jalalabad, Balwinder Singh Dhaliwal from Phagwara, Indu Bala from Mukerian and Sandeep Singh Sandhu from Dakha. The party has 78 legislators in the 117-member House.
The Bharatiya Janata Party's (BJP) alliance partner the Shiromani Akali Dal (SAD) has fielded Manpreet Singh Ayali from Dakha and Raj Singh Dibbipura from Jalalabad.
The BJP has fielded Rajesh Bagga from Phagwara and Jangi Lal Mahajan from Mukerian.
The votes will be counted on October 24.
( With inputs from IANS )