The polling in Kathmandu Constituency No 2, Chitwan Constituency No 4, Bardiya Constituency No 1 and Kailali Constituency No 6, began at 7 am local time, said the Election Commission of Nepal.
The EC has set up 137 polling centres and 324 polling booths. Electronic Voting Machines are being used in all four constituencies.
The by-elections were announced after the leaders of Nepali Congress and Communist Party of Nepal - Unified Marxist-Leninist (CPN-UML) resigned from their respective areas following their win in Constituent Assembly polls last year.
In Chitawan's Constituency No 4, 101-year-old Maheshwor Neupane became the oldest man to cast his vote while Govinda Maya Pradhananga, 95, was the oldest woman voter in Constituency No 2 in Kathmandu district.
The polling is underway in a free, fair and peaceful manner in all the four constituencies, said the Election Commission in a statement.