An imploding cavity in a fluid‐filled borehole is potentially attractive as a powerful source of acoustic energy for borehole seismic experiments. It is reasonable to model the fluid pressure response due to the implosion as purely one‐dimensional. A simple analysis based on the assumption that the fluid behaves elastically, with a linear pressure/strain relation, predicts that the fluid pressure response becomes negative at depths less than that of the source. This is an untenable prediction since a fluid cavitates under negative pressure. It is more realistic to assume that the fluid behaves in a linear elastic fashion for negative strains (and positive pressures), and that the fluid pressure is zero for positive strains. This leads to a nonlinear, free‐boundary problem in acoustic wave propagation, which surprisingly has a closed‐form analytical solution. The analysis predicts the existence of several unexpected phenomena which could complicate the interpretation of data taken in borehole seismic experiments utilizing this type of source.