Kobayashi potential method has successfully been applied to potential as well as scattering geometries containing perfect electrically conducting (PEC) objects by many investigators. The purpose of present study is to extend Kobayashi potential method to study the scattering from non-PEC objects hence, to enhance the applicability of the method. First, geometries containing strip are considered and diffracted fields have been determined from an impedance strip, from a strip placed at dielectric slab and from a perfectly electromagnetic conducting (PEMC) strip. Then slit geometries are included. And studies are conducted to analyze the diffraction from an impedance slit placed at the interface of two different media, from two parallel slits in an impedance plane and from a slit in PEMC plane. While applying this method to above type of problems, diffracted fields are considered in terms of unknown weighting functions. Imposition of boundary conditions give dual integral equations. These dual integral equations are then used to decide the nature of weighting functions by using the discontinuous properties of Weber-Schafheitlin’s integral. Edge conditions are also taken into account at this moment. Finally, matrix equations are obtained to evaluate the expansion coefficients. The elements of these matrix equations are the infinite integrals and are usually, very complex in nature and hard to solve analytically. So these integrals and the matrix equations are then solved numerically for unknown expansion coefficients. Diffracted fields are presented for each geometry. Their dependence on different parameters like angle of incidence, slit/ strip size, impedance of plane, relative permittivity of the surrounding media has been discussed and analyzed. Comparison with physical optics is also presented in some problems to validate the presented results.