Abstract: Differential equations of free/forced vibrations of n-step one-way thin rectangular plates subjected to in-plane tensile/compressive force in y-direction on Winkler’s foundation are established by using singular functions, their general solutions solved for, expression of vibration mode function and frequency equation on usual supports derived with W operator. Influence functions for various cases deduced here may also be used to solve problems of static buckling or stability for beams and plates in relevant circumstances.