Abstract: Vibrations of non-unitary materials n-step one-way rectangular plates are researched. Differential equations of free/forced vibrations for such plates are established by using singular functions, their general solutions solved with method of initial parameter. The traditional solvent of static and dynamic problems for stepped prismatic beams is to set up ordinary differential equation in each step and answer it respectively. That is so troublesome. With W operator, resolution of the former may be expressed with one equation only, and expression of vibration mode function/frequency equations of plate on usual supports derived. Forced responses of like that plates stated here under different-type loads discussed with generalized functions. Influence functions given here are strong tools to settle ordinary differential equations which described in the text. It can also be to deal with problems of static buckling and steadiness of stepped beams or one-way rectangular plates.