In this paper we treat the scattering of electromagnetic waves from a two-dimensional structure consisting of a periodic array of conducting bars of rectangular cross section. The E mode case is considered, in which current essentially flows around each bar, perpendicular to the bar axis. Numerical solutions are obtained based on approximating the currents on each bar by a set of P “triangle” functions. The electric field radiated by the periodic array of triangle current functions is found by standard Fourier series techniques. The field is required to satisfy the boundary conditions in an integral sense over P intervals associated with the triangle functions. The resulting P equations in P unknowns are solved numerically. Finally, a number of examples are analyzed, including transmission gratings and parallel plate polarizers.