Nepinak, 31, went missing in September 2011 and though her remains have never been found, police believe they may be buried somewhere in the city landfill and that she was killed by alleged serial killer Shawn Lamb.
This past summer, police originally identified a large search area but then scaled that back to a five-metre-square space, focusing on an area identified by aboriginal elders who had held a traditional ceremony there.
Police officers wore respirators and biohazard suits as they started sifting through garbage on Wednesday.
Const. Jason Michalyshen, who showed reporters the search area, said it could last three to five days.
"Our commitment to Tanya and the family — and certainly the relationship we have developed with the aboriginal community and the elders that have directed us to this location — our commitment is to complete this search," Michalyshen said.
Lamb, 52, was charged in June with second-degree murder in the deaths of Nepinak and two other women who went missing in Winnipeg.
Police have said they believe Nepinak's body was placed in a garbage bin that was emptied in the landfill.
The search was originally set to start on Tuesday, but gusting winds created safety concerns for the searchers, forcing a postponement.
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