Elastic modeling of a spatially-discrete system can be formulated as an eigenvalue decomposition problem. Using this formulation, the exact solution can be obtained for an arbitrarily complex model, without the need for time discretization. The unavoidable drawback of this formulation is its prohibitively high computing time, which is proportional to N3, where N is the number of cells in the mesh. Building up a discrete physical model has some advantages over the usual numerical discretization of a continuous system. If the physical model is solved exactly, then stability is guaranteed since natural systems are always stable for impulsive sources. In addition, the resulting 2-D differencing star tends to cause less numerical anisotropy than the star obtained by straightforward discretization. An alternative solution in the time domain allows for an effective implementation of the modeling scheme in a massively parallel architecture machine.