Company spokesman Paul McElroy says the two airlines canceled 60 flights by late Saturday morning, six hours after the outage started.
The airline will rebook passengers without a fee. It says customers should call the airline to check on their flight before going to the airport.
McElroy says the airline has been able to operate about 20 flights during the day.
He says the cause of the computer problem isn't known but technicians are working on it.
Seattle-based Alaska Airlines flies to cities in the U.S., focusing on the West Coast, and to Canada and Mexico.