The teleseismic amplitude resulting from an underground explosion is proportional to the asymptotic value of the reduced displacement potential (ϕ∞) or, in physical terms, to the permanent change in volume measured anywhere beyond the range at which the outgoing wave has become elastic. It is known that ϕ∞ decreases with increasing initial cavity size (r0) until the cavity is large enough to preclude inelastic behavior in the surrounding rock, at which point no further decrease occurs. Earlier numerical calculations suggested that ϕ∞ was not a monotonic function of the initial energy density and that the seismic amplitude might actually be decreased, in certain cases, by decreasing the initial cavity size. We have examined this question from an analytical point of view and derived the seismic response for a simple linear-elastic, perfectly plastic medium as r0→0. In this limit, an exact, power law relationship is found between ϕ∞/W and r0W-1/3, where W is the yield, a result which implies that ϕ∞ vanishes altogether for an explosion in which the initial cavity radius is vanishingly small. The physical explanation for this curious behavior is shown to derive from the unique inability of a Hooke's law medium to generate thermal pressure. A similar, but less dramatic, effect is demonstrated with more realistic material models. The significance of these results is that the estimation of yield from measurement of seismic amplitude may be a less accurate process than previously suspected. ¿ American Geophysical Union 1993