The propagation of transient sound waves in bounded one‐ and three‐dimensional regions is studied by means of Laplace transform methods. In the one‐dimensional case, a plane wave is considered propagated down a rigid‐walled tube from a source at one end toward an acoustic termination at the other end. The velocity potential for an arbitrary particle‐displacement input is found as a series, each term of which represents the effect of a reflection from the ends of the tube. In the three‐dimensional case spherical wave from an arbitrary input source is considered, first in an unbounded region, and then in regions containing one wall, three perpendicular walls, and two parallel walls; finally, the case of a point source in a rectangular room is solved. An image method is used, the results being found in the form of a series whose terms represent reflections from individual walls, as well as cross reflections between walls. The terms of the series are in the form of plane‐wave expansions around the image points; these integrals are approximated by the method of steepest descents. In the last section some sample calculations are made for both the one‐ and three‐dimensional systems.