The singularity expansion method is applied to determine the natural resonances of a perpendicular crossed wire structure oriented parallel to an imperfect ground plane. To account for the finite conductivity of the ground, three formulations are utilized. First, the rigorous Sommerfeld formulation is used; then for structures some distance from the ground an approximate Fresnel reflection coefficient approach is employed. For structures in proximity to the ground a lossy transmission line formulation is presented. Sample results from all three formulations are presented.