Transient surface pressures generated by a piston set in a spherical baffle or sonar array are obtained in analytical form for velocity steps and CW pulses. Neither the wave-harmonic series, which converges poorly at early times, nor geometric acoustics, which predicts zero pressure on passive elements, is applicable. A technique successfully used for CW impedance calculations was adapted to transient situations. On passive elements, the pressure is computed from Watson's “creeping-wave” formulation, which fails on the active element; there, the pressure is approximated by ignoring baffle curvature. The required Laplace integrals are available in the literature. Numerical results are presented. [Sponsored by Naval Ship Systems Command, under Computer Applications, Inc. subcontract.]