The Federal Aviation Administration announced on Monday that it would require extensive inspections of some older-model Boeing 737s for cracks in the planes’ fragile skin that can be caused by pressurization and depressurization of the cabin over tens of thousands of takeoffs and landings.

Three days earlier, undetected cracks widened into a five-foot hole in the roof of a Southwest Airlines flight, forcing the plane, a 737-300, to make an emergency landing at a military base. The F.A.A. announcement applies to 175 aircraft worldwide, including 80 that are based in the United States. Most are operated by Southwest, which started inspections over the weekend and has found three more planes with small cracks.

The airline also canceled 70 flights from its schedule of 3,400 departures on Monday. About 300 flights were canceled on both Saturday and Sunday.

The incident on Friday was at least the third involving metal fatigue in the last few years, and the most terrifying. The others involved another Southwest 737-300 flight in 2009 and an American Airlines Boeing 757 last year.