Ground motion prediction formulas based upon elastic wave propagation in one-dimension (no strain transverse to the propagation direction) have been used widely in protective construction work. Actual soil materials exhibit many deviations from elastic behavior. This report assesses the probable influence of these non-elastic effects upon the accuracy of the above-mentioned prediction formulas, and upon the question of stress attenuation with depth. Three different models of soil behavior are assumed: a standard 3-element visco-elastic model (spring in series with spring-dashpot combination); a compacting model (straight line loading and unloading curves); and an ''elastic'' model in which any arbitrary shape may be assigned to the loading stress-strain curve. This report deals primarily with the first of these three models; the possible significance and probable importance of the third model are discussed briefly. By combining the theoretical and experimental results, it is shown that the elastic ground motion prediction formulas are generally valid (for cases where it is appropriate to think of one-dimensional motion); i.e. the possible effects of viscosity and inelasticity are no greater than uncertainties as to the order of magnitude of the compressibility of an in situ soil mass. (Author).