Commuter airlines last night began inspecting their Brazilian-made Embraer Bandeirante planes for possible sheared or worn rivets in the tail section after the Federal Aviation Administration ordered them to do so.

By early afternoon the inspection procedure was in the hands of many of the 17 U.S. carriers flying Bandeirantes. They had 18 flight-hours after receiving the official FAA directive to inspect each plane.

If no problems are found or if repairs are made, the planes may be returned to service. It is estimated that about 60 of some 95 Bandeirantes in commercial service in the United States require the inspection.

Two airlines serving Washington-area airports use the aircraft. They are Newair, which flies between Washington National and New Haven, Conn., and Tennessee Airways, which flies between Washington Dulles and Knoxville. The Bandeirante is a twin-engine turboprop usually fitted with 19 passenger seats.

Several small airlines have reported passenger resistance to flying on Bandeirantes, industry sources said yesterday. "We have had a lot of phone calls from travel agents who want to book around the Bandeirante," one source said.

The concern stems from a recommendation Tuesday by the National Transportation Safety Board that the planes be grounded until inspections were conducted. The FAA elected to permit 18 hours leeway after it had developed precise inspection directions.

The board's recommendation came during its investigation of a Bandeirante accident Dec. 6 in Jacksonville, Fla., that killed 13 people. In that crash, a section of the plane's tail fell off shortly after takeoff, making the plane uncontrollable.