The Sommerfeld-Maliuzhinets method is used to calculate the total fields in the interior and exterior regions of an arbitrarily angled resistive wedge. A E-plane wave (TM mode) normally illuminates the two-dimensional resistive wedge. Two spectral functions are introduced to represent the fields in both regions. By imposing the resistive boundary conditions on the wedge faces, a system of coupled functional equations is obtained for the two unknown spectral functions. The functional equations are reduced to singular integral equations for the auxiliary functions. The predictions for a right-angled resistive wedge are shown to be in good agreement with measurements.