Ruling JD(U) candidate Prashant Kumar Sahi, who is also the education minister, RJD nominee Prabhunath Singh and Jitendra Swami of Congress are the main candidates in the reckoning.
Balendra Kumar Rai, Vikas Kumar Siingh and Om Prakash Singh are the other contestants in the by-poll which is being held after the death of RJD MP Uma Shankar Singh.
Election office sources said the polling was moderate to brisk in 1476 booths in six assembly segments spread in Saran and Siwan districts.
The sources said 20 companies of central paramilitary forces, 10 companies of Bihar Military Police (BMP) and 7000 additional policemen have been deployed to ensure free and fair polls.
The by-poll is being keenly watched by all political contenders as its result would be a reflection of public mood ahead of the 2014 general elections.