An analytical study of threshold resonances in scattering of scalar waves from periodic surfaces is presented. Resonances are found with a variety of line shapes which provide characteristic information on the surface potential. The analytical predictions on line shapes are supported numerically. These resonances should be observed in atom-surface scattering and in scattering of light from large-amplitude gratings. We think that these resonances may be important for the field enhancement on surfaces. © 1982.