This paper presents a finite difference method to solve free and forced vibration problems of rectangular plates with differing boundary conditions. The natural frequencies are obtained from the peaks of the free vibration response in the frequency domain by exciting the plate with an initial displacement. The free vibration response in the time domain is calculated using the finite difference method. This is then converted to the frequency domain using Fourier transform. In this paper, the plate is subjected to various dynamic loadings, namely, a step function, rectangular and triangular loads, and a sinusoidal harmonic loading. The present results are compared to analytical and numerical solutions available in the literature. The results obtained are in good agreement with those of exact and numerical results available in the literature.