Finite difference solutions for the static and dynamic displacements of a plate undergoing vibration are presented. The approach presented differs from the conventional methods in which the derivatives are expressed by their difference equivalents. Here the difference equations are obtained as solutions to the fourth order biharmonic equation. A single space varying drive number is found which varies from node to node and characterizes the true mode shape of the plate at a node. The technique presented can be applied to finite elements of triangular, rectangular or quadrilateral geometry without any restriction. The Marcus difference solution is seen to be a particular case of the general difference solution derived in this paper to give static deflection. The analysis is confined to small deflections of plate but the technique can also be applied to appropriate differential equations for large deflections. The method has applications in the determination of the displacements of structures having arbitrary boundary conditions. Evaluation of complicated modal response associated with the traditional approach is thus avoided.