The Seattle-based airline said the system's functionality had been partially restored by Saturday afternoon - but more cancellations and delays are possible.
The outage began at 3 a.m., disrupting about 15 percent of Alaska Airlines and Horizon Air flights. Some 11,700 passengers were affected.
Technicians partially restored the system by noon, but disruptions continued to plague the airline throughout the day. Specialists will work on permanent repairs overnight Saturday.
So far, 58 Alaska Airlines flights have been cancelled, as well as 81 Horizon Air flights.
Twenty of Alaska Airlines’ canceled flights were departing Seattle while another 10 were in the state of Alaska. The remaining cancellations affected departures throughout the airline’s route system, including six in Southern California, five in Portland and four in the Bay Area.
Horizon has canceled 81 flights so far, including 30 departing from Seattle, 13 in Portland and eight in Spokane.
Presidents of Alaska Airlines and Horizon Air issue a video apology for Saturday's flight disruptions.
"We’re working to get our operation back to normal as quickly as possible and are very sorry for the inconvenience to our customers," Alaska Airlines President Brad Tilden said.
The airlines are also working to accommodate customers on other carriers.
Company spokesman Paul McElroy said many flights were delayed, and customers had trouble getting flight-status updates on the airlines' website because of the outage.
Alaska Airlines advised passengers to check their flight status online or call 1-800-ALASKAAIR before leaving for the airport. The airline says it will rebook passengers without a fee.
The computer system went down about 3 a.m. Saturday when a backup power system upgrade was being installed and a transformer malfunctioned.
During the outage, passengers reported that Alaska Airlines was unable to print boarding passes at some airports, and gates were filling up with passengers. Passengers were allowed to board some planes, but they remained sitting on the tarmac.
At Sea-Tac Airport, Alaska's flight information boards were turned off during the outage to avoid confusing passengers.
"The flight information boards were actually turned off most of the time because they were so inaccurate, they didn't have information on them, and they were just confusing passengers," said John Locher, who was waiting Saturday morning at Sea-Tac to board an Alaska Airlines flight to Orlando, Fla.
He and other passengers said they wished the airline would have released more information during the outage.
"Alaska is a good airline. Just treat us like adults and give us more information, and we'll be grateful," Locher said.
He said his flight was supposed to leave at 8:50 a.m. but still had not boarded by 11 a.m.
Seattle-based Alaska Airlines flies to cities in the U.S., focusing on the West Coast, and to Canada and Mexico. Alaska and Horizon are owned by Alaska Air Group Inc.