The problem of plane monochromatic linearly polarized electromagnetic wave diffraction through a stratified medium is solved by means of general solution expansion on fundamental solutions system for each separate polarization. In case of isotropic media the problem is equivalent to one of solving a linear algebraic equations system – two boarder equations on each boarder. In case of general monochromatic polarized electromagnetic wave the problem is equivalent to the solution of linear algebraic equations system with four equations on each boarder. In case of anisotropic media the method of the solution is the same, the difference is in that four equations on each boarder form a matrix without zero blocs.