Phase screen simulations of vector wave propagation in elastic random media are applied to two independent studies of seismic wave scattering. In the first study, transmission fluctuations are analyzed for incident P waves, propagated through a two-dimensional version of the two-layer model of Flatt¿ and Wu (1988) of the crust and upper mantle beneath NORSAR. Numerical stimulated coherence functions for vector elastic waves are compared to analytic and simulated results based on the parabolic approximation to the scalar wave equation. The usefulness of phase screen simulations for analyzing fluctuations for moderately strong scattering (~2%--5%) perturbations), and for three-component data, is demonstrated. In the second study, effects of multi-scale random structure on the variances of the initial P wave peak-to-peak amplitude and the rms amplitude of the transverse components in the velocity window between the average P and S wave speeds are investigated. A large number of synthetic seismograms are generated for eight random media models. This study shows that the relative variance of the rms scattered phase is far less dependent on the model than that of the direct phase. The variance of the forward scattered P wave depends greatly on the strength of the large-scale heterogeneities. ¿American Geophysical Union 1993