Abstract: The difficulty of singular integral is met with in the computation of electromagnetic scattering by surfaces of arbitrary shape using the model presented by S.M.Rao. In this paper an analytical algorithm with high precision and speed is proposed. The question is first transformed from the global three dimensional rectangular coordinate system to a local two dimensional polar coordinate system by shifting and rotating the coordinates. As a result, the singular point is eliminated, so the intermediate result of singular integral can be analytically worked out. Then the value of the singular integral of the original question is obtained by the transformation of coordinates inversely. To prove the validity of this method, the distribution of current density on surfaces of conducting square flat plate, bent plate and sphere are computed. The results are in good agreement compared with those from related references.