The two planes will be evaluated further and more repairs will be made before they are returned to service, Southwest said.
Friday's flight carrying 118 people lost cabin pressure after the Boeing 737-300's fuselage ruptured -- causing a 5-foot-long tear -- just after takeoff from Phoenix.
Passengers recalled tense minutes after the hole ruptured overhead with a blast and they fumbled frantically for oxygen masks. Pilots made a controlled descent from 34,400 feet into a southwestern Arizona military base. No one was seriously injured.
The tear along a riveted "lap joint" shows evidence of extensive cracking that hadn't been discovered during routine maintenance before Friday's flight -- and probably wouldn't have been unless mechanics had specifically looked for it, officials said.
National Transportation Safety Board investigators on Sunday were in Yuma, Ariz., to oversee the removal of the top section of the jetliner's roof around the tear.
The structure will be sent to Washington for analysis.