Almost all known photoacoustic image reconstruction algorithms are based on the assumption that the acoustic waves leave the object (the imaged region) after a finite time. This assumption is fulfilled if the measurements are made in free space and reflections from the detectors are negligible. However, when the object is surrounded by acoustically hard detectors arrays (and/or by additional acoustic mirrors), the acoustic waves will bounce around in such a reverberant cavity many times (in the absence of absorption, forever). This paper proposes fast reconstruction algorithms for the measurements made from the walls of a rectangular reverberant cavity. The algorithms are tested using numerical simulations.