The behavior of variable thickness laminated composite beams has not so far been fully understood. In the present thesis, a finite element formulation is established for uniform and variable thickness composite beams (externally and mid-plane tapered composite beams). First the conventional formulation is used to establish the stiffness, geometric stiffness (for constant axial load, uniformly distributed axial load, and non-uniformly distributed axial load), and mass matrices. Second a new formulation (advanced formulation) is established, which considers not only the geometric boundary conditions, but also the natural boundary conditions. This means that at each node there will be four degrees of freedom, that are deflection, slope, bending moment, and shear force, such that all physical parameters that can be encountered in any practical situation can be included in the element formulation. The new stiffness, geometric stiffness, and mass matrices corresponding to the new formulation are set up. These matrices are provided into the MATLAB ® environment to obtain the natural frequencies and the critical buckling load.