The Monte Carlo technique is proposed for the determination of the acoustical pressure‐time history at chosen points in a partial enclosure, the central idea of this technique being the tracing of acoustical rays. A statistical model is formulated and an algorithm for pressure is developed, the conformity of which is examined by two approaches and is shown to give the known results. The concepts that are developed are applied to the determination of the transient field due to a sound source in a homogeneous medium in a rectangular enclosure with perfect reflecting walls, and the results are compared with those presented by Mintzer based on the Laplace transform approach, as well as with a normal mode solution. In contrast with these, the Monte Carlo method is not restricted to the case of perfectly reflecting walls, since absorptive walls can be handled. Possible future developments are indicated which would, it is believed, make the Monte Carlo method a valuable tool when boundary conditions are complex or when the medium is inhomogeneous.