Many of these seats are located in areas which had earlier witnessed Maoist violence.
Election Commission sources said there was no report of any violence or disturbance from anywhere.
Polling will be held in another 31 seats in second part of the first phase to be held on April 11.
Of the 18 constituencies which went to polls today, 13 are located in tribal Jangalmahal spread over Bankura, Purulia and West Midnapore districts.
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People came out in large numbers since early morning to cast their votes, EC sources said.
"There were some issues with EVMs in some booths which were immediately addressed and polling went on smoothly. We got some other complaints also and they have been addressed," Additional Chief Electoral Officer Dibyendu Sarkar told PTI.
Polling began at 7 AM under tight security. Two choppers conducted regular sorties as part of aerial surveillance.
Voting was held in 4,945 polling stations out of which 1,962 were classified as critical by EC.
A key candidate in this phase was Tribal Affairs Minister Sukumar Hansda from Jhargram.