DALLAS — Southwest Airlines Co. said Monday that most of the planes it grounded over the weekend were back in the air after being inspected for microscopic cracks in the aluminum skin.

That will get Southwest back on a full schedule today after nearly 700 flights were canceled and others suffered delays over three days.

It is less clear whether Southwest’s reputation will recover as quickly after one of its planes sprung a hole in the roof Friday and three others were found to have cracks that will keep them out of service.

Some stranded passengers were angry with Southwest and threatened to switch airlines, but others praised the company’s decision to ground planes as a safety-first precaution. Southwest had a similar incident with the same model of 737 in 2009 and the airline didn’t seem to suffer for long, if at all. Lately, traffic on Southwest has grown faster than on other airlines.

Southwest appeared eager Monday to shift blame to Boeing, manufacturer of the 15-year-old 737-300 that had to make an emergency landing in Arizona after a 5-foot-long tear developed in the roof.

The airline said it had never been told of a potential problem where overlapping panels of aluminum skin are riveted together on the 737-300.

“This is a Boeing-designed airplane. This is a Boeing-produced airplane,” said Southwest spokeswoman Linda Rutherford. “It’s obviously concerning to us that we’re finding skin-fatigue issues.”

Blaming Boeing, however, is a juggling act for Southwest. The airline may want to deflect criticism, but it would suffer if passengers believe Southwest’s planes are not safe. Southwest has built its operation around the simplicity of flying only one plane, the 737, and it likely will still have the older 300s in its fleet for several more years.

Boeing officials declined to respond to Rutherford’s comments, but the company has plenty at stake. Boeing could wind up in a public spat with its biggest customer, and the legacy of its best-selling plane could suffer a black eye.

Still, it’s been 11 years since Boeing delivered the older type of 737 that will be subject to inspections under a new federal order due out today.

Robert Mann Jr., an aviation consultant in Port Washington, N.Y., said Friday’s incident would not cause lasting harm to Southwest’s reputation, partly because the airline moved quickly to ground and inspect planes that might have the same weakness.

“There was nothing Southwest failed to do or did improperly,” Mann said. “This was something no one had seen before.”

Southwest grounded 79 planes over the weekend after passengers on the Phoenix flight heard a loud bang and saw sky through a gash in the roof at 34,000 feet. The plane made an emergency landing, and Southwest said no one was seriously injured. The jet had made nearly 40,000 takeoff and landing cycles.

Late Monday, Southwest said it had inspected 64 of the planes and put them back in service. Three others need repairs after tiny cracks were detected using electromagnetic tests.

Earlier, the Federal Aviation Administration said it will require special inspections aimed at finding metal fatigue in some Boeing 737s. The FAA said the order will affect about 175 planes worldwide. That includes 80 registered in the United States. Southwest operates nearly all of those.

The airline believes its own inspections over the weekend will meet the FAA requirements.

Some Southwest loyalists were quick to defend the airline.

Linda Tripoli, who said she uses Southwest every other week in her job with a medical emergency communication com- pany, praised the airline for grounding many of its planes for inspections.

“They’re making sure we’re safe. Every airline has had a hiccup,” said Tripoli, who noted that Southwest has never had an accident-related death on board a plane. (A 6-year-old boy in Chicago was killed in 2005 when a Southwest jet skidded off the runway and struck the car in which he was riding.)

But a stranded passenger, Shelly Simone of Chicago, was steaming after she and her two children were forced to spend another night in Florida and Southwest wouldn’t reimburse her for lodging. The airline put her on a Monday night flight.

Simone said Southwest wouldn’t cover her expenses for a flight canceled due to mechanical reasons. “I don’t know how they can say that’s not their fault,” she said, and added that she might start flying other airlines more often. Southwest did not respond for comment on Simone’s claim.

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