The basic equations are derived using one of existing techniques. The general solutions in terms of three arbitrary functions of the dynamic equations of equilibrium taking into account displacement are used. An algorithm is developed using computer stability within a small neighbourhood of the surface z=0. When using this algorithm the numerical results of an analysis of strained-stress state are presented for the thick three-layer plate with bearing layers of steel under steady forced vibrations. It is concluded that the new static and dynamic problems of multilayer plates and shells can be solved via method of initial functions.