In this paper, finite element method is applied to structural analysis of rectangular plate subjected to different boundary conditions. The governing equation of motions for the static analysis of a rectangular plate are developed using Kirchhoff plate bending theory. The verification and the reliability of the finite element methods used is established by comparing the results of an in-house MATLAB code and that of commercial computational solid mechanics code using FLEXPDE as well as exact analytical method. The results of the exact analytical method, MATLAB finite element method and FLEX finite element method show excellent agreements. Also, it was observed that the boundary conditions and the dimensions of the plate have significant influence on the vibration of plates. The results showed that Clamped- Simply Supported - Simply Supported -Simply Supported (CSSS) mixed boundary condition gave the highest deflection for each thickness and loading type while the Clamped-Clamped- Clamped -Simply Supported (CCCS) mixed boundary condition provided the lowest deflection. The FEM algorithm developed in this project shows great agreement with commercial software results. It is inferred from the study that use of the developed finite element codes in MATLAB is an easier, cheaper and quicker approach for the analysis of free vibration of an isotropic rectangular plate.