The metallic diffraction grating problem has been solved for P-polarization using a conformal mapping and the surface impedance boundary condition. The method is used to calculate the electromagnetic fields diffracted by a grating having a cycloidal groove shape. The numerical results are compared with those obtained using the direct differential formalism. For low conductivities the coincidence between both results is only qualitative, whereas there exists a zone for greater conductivities where the differences are smaller than 0·;005. For even greater conductivities the approximated boundary condition employed holds more exactly, but the comparison is not possible because the direct differential method involves numerical problems.