This post has been updated. See below for details.
The airline, which has roughly 3,200 flights per day, said the system went down about 8 p.m. Pacific Standard Time.
Planes already in the air were not affected.
Southwest spokeswoman Michelle Agnew said airports on the West Coast, in the Mountain states and even some in the Midwest have been affected. But she could not specify how many flights have been grounded.
"We're not able to give a number because we're not able to see how many flights we've got on the ground right now," Agnew said.
In Los Angeles, airport officials reported that 13 Southwest flights had been scheduled to depart from
At L.A./Ontario International Airport, three flights were affected, according to officials with Los Angeles World Airports, the agency that runs LAX and Ontario airports.
Southwest officials have not decided whether or not to cancel the flights entirely, Agnew said. The company's Facebook page quickly began filling up with complaints from customers sitting in planes parked at airport terminals.
[Updated, 11:02: Finance manager Scott Williams said that by 10:30 p.m., he had been sitting in a Southwest plane at Ontario Airport for nearly three hours.
At one point, half the passengers were told to get off the plane and return to the gate, said Williams, of Napa.
"Then they hurried everyone back onto the plane in the hopes of departing," he said. "I'm personally not that optimistic that it's going to happen."]