A study of buckling and free vibration of rectangular Mindlin plates is presented. The analysis is based on the pseudospectral method, which uses basis functions that satisfy the boundary conditions. The equations of motion are collocated to yield a set of algebraic equations that are solved for the critical buckling load and for the natural frequencies in the presence of the in-plane loads. Numerical examples of rectangular plates with SS-C-SS-C boundary conditions are provided for various aspect ratios and thickness ratios, which show good agreement with those of the classical plate theory when the thickness ratio is very small.