UPDATED 04/04/11 4:45 p.m.

CHICAGO (CBS) — Southwest Airlines says jetliner inspections will continue Monday and could be finished by late Tuesday, in the wake of last week’s accident and emergency landing involving one of its 737-300s.

As CBS 2’s Susanna Song reports, Southwest says it canceled 70 flights on Monday, which include several at Midway International Airport.

Passengers at Midway said Monday they are concerned, but not scared enough not to fly.

Lisa Schaible says she is “crossing her fingers.” She is sending her 10-year-old daughter on a flight to Baltimore by herself.

“It’s a little nerve-wracking,” Schailbe said.

Schaible’s daughter, Kayli, says of the plane on which she is about to fly, “I hope they checked it good.”

Kayli says she will hold onto her ne American Girl doll closely, but in the end, her mother says she trusts Southwest will be extra-careful.

“They will have checked everything, so you would think it would be safer to fly now,” she said.

Nearly 900 of the Boeing 737-300s are in use around the world, and more than 200 of them are in the United States. Some are 20 years old and have flown thousands of times.

“With airline safety, what’s notable is how hard we’re running the system, and  I think we’re seeing new kinds of maintenance issues crop up,” DePaul University aviation expert Joe Schwieterman told CBS 2’s Jim Williams.

Southwest passenger Jennifer Stevens says she is not worried, though.

“I actually work for a company that underwrites aviation liability, and Southwest is one of the safest companies out there,” she said.

The problems began Friday, when a rupture in the ceiling forced a Southwest flight from Phoenix to Sacramento had to make an emergency landing in Yuma, Ariz.
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None of the 118 people on board was seriously hurt, but many people were terrified.

“I just heard a bang… all of a sudden all the (oxygen) masks dropped, and everyone was trying to put the masks on, and it was scary,” passenger Brenda Reese said.

Federal investigators now want to know what caused the fuselage to break apart in that plane, and caused tiny cracks in three others.

“It will undergo intense, in-depth analysis once it gets back to Washington,” said Robert Sumwalt of the National Transportation Safety Board.

On the plane that made the emergency landing in Arizona, quarter-inch cracks were discovered along the joints that run the length of the aircraft. The NTSB has never mandated checks in that area, but officials say that could change.

“There are methods using technology to inspect, and just in this industry, it was not thought that this was an area that needed to be inspected,” Sumwalt said.

Back at Midway Monday morning, Jennifer Boude and her 14-month-old son were heading home to San Antonio, Texas. They were feeling confident.

“I take it in good faith that they’re grounding the planes that need to be grounded and have checked the planes that are flying,” Boude said.

Added Sue Chun, who was heading to Washington, D.C., with friends: “I’m still going to take a chance and go. Hopefully, everything will be OK, I have think positively.”

“I’m sure they’ll check ours,” added Jeff Sturmon, who was off to Tucson, Ariz. “I’m sure southwest isn’t the only airline that has problems.”

Over the weekend, 600 Southwest flights were canceled, and more cancellations are expected through Tuesday.

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