An analytic model (Bote model) is presented as a means to describe the pressures at and arrival time of the spherically diverging stress wave resulting from an underground explosion. The model is based on a linear combination of the forms used to describe the two extremes in the stress wave lifetime: a strong shock at early times and a simple elastic wave at late times. The Bote model traces the propagation of the spherically diverging stress wave through the hydrodynamic, plastic, crush-up, and elastic pressure regimes and predicts the pressures at and arrival times of the shock front. While able to account for the effects of porosity and water content of the surrounding medium, the Bote model requires knowledge of only two points on the pressure-volume (PV) curve of the medium: the pressure PE below which the medium is assumed to behave elastically and the pressure PC at which all air-filled voids in the medium have been crushed out. Simple expressions are given for determining PC and PE as a function of water content and gas fill porosity. Other necessary Bote model inputs include explosive yield (Y) and medium type as well as geologic characteristics, including grain density (&rgr;g), in situ density (&rgr;0), water content (W), and sound speed (C). Compared with both calculated and measured ground motion data, Bote results show good agreement for times ranging from tens of microseconds to tens of milliseconds, for distances out to a scaled range of 107 m/kt1/3, and for pressures to of the order of 105 Pa.