Both an infinite-series solution and a finite-difference solution have been obtained to the problem of elastic response of a complete, thin, spherical shell to axisymmetric transient pressure loading. The two solutions are compared to each other for two specific examples and are also compared with previously published experimental data for one of the examples. The authors conclude that either solution is usable for engineering predictions of dynamics shell response. They also recommend conduct of more carefully controlled experiments for comparison with theory.