A dud shell of World War II vintage whistled through the sky and landed with a ''resounding crash'' on a back- yard patio, leaving a crater four feet deep, officials said today.

A Los Angeles County sheriff's bomb squad dug up the unexploded shell Sunday and determined that it contained no explosives, Deputy Stephen Lee said.

The Federal Aviation Administration and the Sheriff's Department believe the shell was dropped by a prankster, but no one reported seeing a plane, said Deputy Wes Slider.

The 22-pound missile struck about 4 P.M. in the yard of Fred Simons, 79 years old.