A solution methodology is developed to solve plane stress problem of composite plates with variable stiffness by using Galerkin technique and polynomials as trial functions. in the solution process, analytical computation has been done wherever it is possible, and analytical-numerical type approach has been made for all problems. The methodology is applied to two known case problems, composite plate with variable fibre content and laminated plate with spatially varying fibre orientations. The formulation of these problems results into coupled partial differential equations (with variable coefficients). The solutions of these equations are obtained using the polynomials as trial functions in the Galerkin method. The results are compared to that of Ritz and collocation technique published elsewhere. The method is found to determine closely both the displacements and the stresses with a few number of terms and in good agreement with other approximating methods. Computations on some examples show that, the method with the help of a symbolic math package is simple and efficient for solving these types of problems in engineering applications.