An algorithm is developed to analyze the dissipation of electromagnetic power in waveguide of arbitrary cross section, based on the finite-element method and the Galerkin principle. This procedure is applicable to inhomogeneous media characterized by their loss tangent and resistivity. The wave equation, which is complex due to the presence of dissipative media, is discretized into a complex matrix eigenvalue problem. This matrix system is solved by an iterative procedure with the aid of the Newton-Raphson method, reducing the complex matrices simultaneously, one to upper Hessenberg form and the other to upper triangular form. To verify the accuracy of this method the fundamental mode of propagation in a rectangular waveguide with conductive walls with a slab of dissipative material placed along the symmetry plane of waveguide is analyzed. An image line formed by a silicon rod with two different values for the loss tangent (5.0 × 10-4; 1.0 × 10-3) is also studied.