Solution of large eigenvalue problems is time consuming. Large eigenvalue problems of discrete models can occur in many cases, especially in Finite Element analysis of structures with large number of degrees of freedom. Many studies have proposed reduction of the size of eigenvalue problems which are quite well known today.  In the current study a survey of the existing model reduction methods is presented. A new proposed method is formulated and compared with the earlier studies, namely, static and dynamic condensation methods which are presented in detail. Many case studies are presented.  The proposed model reduction method is based on the boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. This method is extended to discrete models and the admissible functions are replaced by vectors. Gram-Schmidt orthogonalization was used in the first case study to generate the orthogonal vectors in order to reduce a building model.  Further, a more general method is presented and it is mainly used to reduce FEM models. Results have shown many advantages for the new method.