Sattering problem of electromagnetic waves by periodic strip grating with two dielectrics over a ground plane in case of oblique incidence and arbitrary polarization is analyzed by the vector floquet mode expansion method and the moment mehtod from the viewpoint of soft and hard boundary value problem. To confirm proposed analysis methods, we examine the solution convergence for the scattering problem. And some numerical results of artificially soft and hard surfaces using the structure filled with single dielectric slab between periodic strip grating and gorund plane is compared with previous results. Some interesting results for soft and hard surfaces using periodic strips loaded with two layered dielectric slabs over a ground plane are given.