We discuss an approximate analytical model for the hydrodynamic evolution of the shock front produced by a spherically symmetric explosion in a homogeneous medium. The model assumes a particular relation between the energy of the explosion, the density of the medium into which the shock wave is expanding, and the particle speed immediately behind the shock front. The assumed relation is exact for shock waves that are strong and self-similar. Comparison with numerical simulations indicates that the relation is also approximately valid for shock waves that are neither strong nor self-similar. Using the assumed relation and the Hugoniot of the ambient medium expressed as a relation between the shock speed and the postshock particle speed, one can calculate the radius and other properties of the shock front as a function of time. The model also allows one to investigate how the evolution of the shock wave is influenced by the properties of the ambient medium and how these properties affect the characteristic radius at which the shock wave becomes a low-pressure plastic wave. The shock front radius versus time curves predicted by the model agree well with numerical simulations of explosions in quartz and wet tuff and with data from four underground nuclear tests conducted in granite, basalt, and wet tuff when the official yields are assumed. When the model is used instead to fit radius versus time data from the hydrodynamic phases of these tests, it gives yields that are within 8% of the official yields when piecewise-linear approximations to the Hugoniots are used. This accuracy is comparable to the accuracy of other models. ¿ American Geophysical Union 1992