In order to better assess the performance of wireless communication systems,it is desirable to produce multiple Rayleigh fading envelopes with specified correlations. In this paper,we analyze theoretically a procedure which generates correlated Gaussian random variables from independent Gaussian random variables and give a physical explanation for the limitation of this procedure. Then,based on some uncorrelated Rayleigh fading envelopes,a simple but efficient procedure for generating an arbitrary number of cross-correlated Rayleigh fading envelopes is proposed. Simulation results and computational complexity analysis are presented,which show that the proposed method has some advantages,such as high accuracy,low computational complexity and easy implementation,over the conventional simulation method.