An efficient numerical method which can calculate the natural frequencies and mode shapes for very large structural systems is presented. This method applies the accelerated Newton-Raphson method to eigenproblems. If eigenvalues are not multiple, this method can calculate the natural frequencies and mode shapes without any numerical instability which may be encountered in the inverse iteration method with shift. The efficiency of this method is verified by comparing convergence and solution time for numerical examples with those of the well-known methods such as the subspace iteration method and the determinant search method. (C) 1997 Elsevier Science Ltd.