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This report describes an investigation into one-dimensional stress wave propagation in granular materials with microstructure. The study employs the distributed body concept advanced by Goodman and the associated wave propagation studies conducted by Nuniziato, Walsh, et al. A one-dimensional computer program, referred to as MIC1D, has been developed for studying wave propagation in granular materials due to airblast loading. This program allows for: (1) arbitrary surface airblast loading, (2) depth-dependent volume distribution function simulating gravity effects in a granular mass, and (3) treatment of grain size and local porosity as random variables. It incorporates three forms of depth-dependent volume distribution functions, i.e., a periodic form, and exponential form, and a combined periodic-exponential formulation. The user can select any of these forms for the particular application at hand. The probabilistic treatment of grain size and local porosity is accomplished by using a moment-generating procedure due to Rosenblueth. The computer program calculates the expected value and the variance of the output quantities, such as stress and particle motion, due to the randomness in these variables. Application of the computer program is demonstrated by presenting the results of a series of parametric calculations dealing with propagation of acceleration waves in granular media. Documentation of MIC1D is provided in an Appendix.