Two pseudo-spectral implementations of 2-D viscoacoustic modeling are developed in a distributed-memory multi-processor computing environment. The first involves simultaneous computation of the response of one model to many source locations and, as it requires no interprocessor communication, is perfectly parallel. The second involves computation of the response, to one source, of a large model that is distributed across all processors. In the latter, local rather than global, Fourier transforms are used to minimize interprocessor communication and to eliminate the need for matrix transposition. In both algorithms, absorbing boundaries are defined as zones of decreased Q as part of the model, and so require no extra computation. An empirical method of determining sets of relaxation times for a broad range of Q values eliminates the need for iterative fitting of Q-frequency curves.