A regularization-based numerical solution is obtained for arbitrary-shape conic section profile reflector antenna in 2-D, for the H-polarization case. New point is that the reflector surface is assumed a resistive-type material. The problem is treated by reducing the singular integral equation obtained from the boundary condition to the dual series equations and application of the Riemann Hilbert Problem (RHP) technique. The resulting matrix equation has regularized form. Sample numerical results are obtained for various values of the eccentricity of the conic section contour of reflector and the resistivity of its surface. © 2008 IEEE.