The elections come four years after the Sri Lankan army defeated Tamil Tiger rebels in the Northern province, the BBC reported.
Some voters said they hope the outcome of the elections will give a greater voice to Sri Lankan Tamils.
"We want a settlement for the Tamils. That's why we came to vote this time. We've been waiting so many years -- now we want peace," one woman told the BBC.
Voters, who are selecting 38 provincial councilors, are expected to back the Tamil National Alliance, a political party once linked to the rebels, the BBC said.
The United Peoples' Freedom Alliance is the TNA's main rival.
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