Acousticians have largely overlooked the methods ofcomputational fluid dynamics(i.e., the direct numerical integration of the nonsteady, compressible continuity, momentum, and energy equations) because of the success of the linearized normal‐mode approach and because the numerical viscosity inherent in traditional computational methods damp out acoustic disturbances at an unrealistic rate. The advantage of the computational approach is that it allows inclusion of physical phenomena excluded from the linearized normal‐mode approach such as nonlinear convection, nonisentropic losses, and phase change effects. The recent development ofSHASTA, a relatively nondiffusive computational method [J. P. Boris and D. L. Book, J. Comp. Phys.11, 38–69 (1973)], has made possible the accurate solutions to acoustics problems.SHASTAis applied to a piston driven shock wave, an acoustic traveling wave, and an acoustic standing wave. The solutions of these problems by other standard numerical schemes are shown for comparison. It is found that onlySHASTAis acceptable for all problems considered. As a practical example the computational approach is applied to the acoustic‐wave/entropy‐wave interaction associated with reflections from a choked flow wall. [Work supported by DARPA.]