The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that orthogonal polynomials yield superior results for the lower modes. Also, the overall CPU time consumed to perform the calculations by the two different procedures for constructing the approximating functions showed that orthogonal polynomials are computationally more time efficient. A novel approach is devised for the construction of characteristic beam functions for buckling and vibration analysis of an angle ply symmetric laminated composite plate. Numerical results are presented and discussed