The Subspace Iteration Method is a popular approach to obtain the dominant eigenvalues and their corresponding eigenvectors of a given matrix. We have applied this method, making use of two Rayleigh-Ritz projections, to obtain the dominant Lambda Modes of a nuclear power reactor. Also, we have developed a variational acceleration technique for this method, and we have stated that this variational acceleration is very convenient, mainly, when the required number of eigenvalues is low. (C) 1998 John Wiley & Sons, Ltd.