A time domain numerical procedure is presented for a simulation of acoustic-wave phenomena. The technique is an adaptation of the finite-difference time domain (FDTD) approach usually applied to model electromagnetic waves. Simple illustrations of propagation in a nondissipative, infinite, homogeneous medium are provided. In scattering by a soft target the interior fields show that for an acoustically denser target the wave penetrates the target with a magnitude greater than the incident-wave amplitude. Also, the interior acoustic pressure field consists of a pair of high-pressure bands sandwiching a low-pressure band.