While exact techniques are available for plane-wave propagation in uniform flow, acoustic propagation in nonuniform flow has proven much less tractable. A numerical technique has been developed to treat the simplest possible case: acoustic plane waves launched into a uniform shear. The computations are based on the Euler and continuity equations, using only the standard linearization for small acoustic amplitudes. When nondimensionalized, these equations produce a single governing parameter: m/f, where m is the flow's shear rate, and f is the acoustic frequency. Numerical solution for acoustic fluctuation velocity and density at each grid point allows wavefront location and orientation as well as wave strength to be determined. The results for wavefront location and orientation from the current numerical method are compared to a WKB solution obtained from the simplest nonuniform flow approximation which uses a nonuniform speed of sound in lieu of a nonuniform background flow. Gradients of acoustic field variables along the wavefronts, which are not predicted by the standard approximation, are also presented. The acoustic vorticity field is examined to study the rotational nature of the plane waves after interaction with the shear.