The first box was stolen Dec. 19, the Anchorage Daily News reported. The last two disappeared Christmas Eve or Christmas Day.
Investigators say the thefts would have been difficult for a single person to carry out. They say thieves are using chemicals to erase the payees and amounts on checks and then forging new ones and also using account numbers to forge new checks.
Local police and postal inspectors are investigating.
"We've had a couple of victims call in and say, 'That wasn't my check but it's another check that cleared my bank account because it had my account numbers on it," said Detective Michele Logan of the Police Department's financial crimes unit.
Police have identified at least one suspect, who has convictions for drugs and auto theft. The suspect allegedly cashed a check for $358.88 made out to himself that had originally been a payment by an Anchorage man of $54 for his military life insurance premium, an affidavit filed to support an arrest warrant stated.
The suspect hadn't been arrested as of late Thursday.
Anchorage residents are being warned to take their mail to the post office instead of dropping it in a box.