The properties of radiation from a parallel-plate waveguide with an arbitrarily flanged surface of finite size are investigated by means of the boundary element method (BEM) based on guided-mode extracted integral equations (GMEIEs). The reflection coefficient, the reflected and radiated powers, as well as the radiation pattern are numerically calculated for the incidence of a transverse magnetic guided-mode wave. For a number of cases of flanged parallel-plate waveguide, a variety of interesting phenomena have been presented numerically. These effects may be important in the design of antenna systems.