Since the introduction of the expectation-maximization (EM) algorithm for generating maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in emission tomography, there have been many investigators applying the ML method. However, almost all of the previous work has been restricted to two-dimensional (2D) reconstructions. The major focus and contribution of this paper is to demonstrate a fully three-dimensional (3D) implementation of the MAP method for single-photon-emission computed tomography (SPECT). The 3D reconstruction exhibits an improvement in resolution when compared to the generation of the series of separate 2D slice reconstructions. As has been noted, the iterative EM algorithm for 2D reconstruction is highly computational; the 3D algorithm is far worse. To accommodate the computational complexity, the authors have extended their previous work in the 2D arena and demonstrate an implementation on the class of massively parallel processors of the 3D algorithm. Using a 16,000 processor MasPar machine, the algorithm is demonstrated to execute at 1.24 S/EM iteration for the entire 64*64*64 cube of 64 planar measurements obtained from the Siemens Orbiter rotating camera operating in the high-resolution mode.