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We present parallel pseudospectral seismic modeling results for the elastic, variable-density acoustic and constant-density acoustic wave equations on the Marmousi2 model. We focus on the parallel implementation on distributed-memory systems to explore the potentials of the pseudospectral method for large scale seismic simulations. The numerical results demonstrate superior accuracy of the pseudospectral method and good scalability on a Linux cluster, which suggest the promising extensions of the current work to solving 3D seismic modeling and imaging problems on supercomputers.