The radiation and scattering characteristics of a metal-strip grating of finite extent printed on the surface of a dielectric waveguide are analyzed within a two-dimensional model. The diffraction properties are obtained from a solution to the problem of surface mode scattering by a finite number of metal strips, taking into account their mutual couplings. The analysis is based on the electromotive force technique which does not require a grating to be periodic. Obtained results concern the antenna applications of radiating gratings excited by the dominant TE or TM surface mode of the wavegude. The proposed approach can be applied not only to the design of radiators but also filters based on periodic strip gratings.