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The main purpose of this study is to consider an uncoupling method for analyzing explosively loaded structures embedded in hysteretic media. The method, which is based on wave propagation considerations, can be viewed as the plane wave approximation extended to nonlinear problems. Free-field data (both traction and velocity vectors) must be known in order to apply the method. Accuracy of the approximation is shown to be quite good when applied to a series of one-dimensional soil-structure interaction problems, even when the structure and surrounding soil are both nonlinear. Multi-dimensional problems, and techniques for improving the method, are also discussed briefly.