Phase screen, fourth-order finite difference (FD), and eigenfunction expansion calculations of scalar wave propagation in two-dimensional (2D) inhomogeneous media are compared to assess the accuracy of the phase screen method. The phase screen method is a forward propagation (one-way wave) algorithm. The finite difference and eigenfunction expansion calculations, which are solutions of full wave equation, are chosen as references in this study. Comparison of synthetic seismograms by phase screen and finite difference methods is made for four kinds of models: (1) multi-uniform-cylinder model, (2) Gaussian random media, (3) exponential random media, and (4) flicker-noise random media. Results show good agreement for weak random media (velocity perturbations ≦10%). For discrete heterogeneities, such as the multi-uniform-cylinder model, the results agree well for up to 50% deviation in velocities. The computer CPU time of the phase screen program for a problem of grid size 1024 by 512 is 367 sec in a SUN SPARC station II, about 57 times faster than the FD program we used. For large 3D problems the time saved is expected to be much greater. For a single cylinder scatterer with and without absorption, we compare synthetic seismograms by the phase screen method and by the eigenfunction expansion method (exact solution). The agreement between the two methods demonstrates that the phase screen method can also give good results for inhomogeneous absorbing media.