Abstract: Two methods for random field simulation， i.e.， covariance matrix decomposition method and spectral representation method (SRM) areintroduced, their merits and disadvetoges are presented and commented in detail. An example is given to show the use of these two methods in the failure probability calculation of an embankment. The calculation result shows that the SRM needs relatively few steps of simulaton and is much more efficient than covariance matrix decomposition method.