A phase screen method for vector elastic waves is developed. The method allows rapid calculation of the propagation of elastic waves for problems where backscatter is small; only forward propagation is included in the analysis. The method can be used for propagation through either deterministic or stochastic media. The work described here generalizes existing phase screen methods for scalar waves, accounting for the difference in phase velocities of the transverse and longitudinal polarizations. The method is tested on a two-dimensional problem, whose exact solution is also computed, for constant Poisson ratios. Synthetic seismograms for two-dimensional random media using this method are compared with existing finite difference synthetics. An important use of the method is to estimate the rate of interconversion of S and P waves in terms of the energy flux to analyze the effectiveness of potential discrimination techniques. ¿ American Geophysical Union 1991