In this work, the two- (2D) and three-dimensional (3D) population balance models of an MSMPR crystallizer have been developed in order to conduct linear stability analysis. A quantitative comparison of the one-dimensional (ID), 2D, and 3D models has been conducted to determine the range of applicability of these models in terms of prediction of the stable behavior of crystallizers. Both dynamic and steady-state models have been solved for two crystals of practical importance:,64,glutamic acid and hydroquinone, whose nucleation and growth models are well-known. It has been shown that the ID and 2D models agree in terms of stability if the exact shape factor is supplied to the 1D model. If the shape factor is taken to be unity, inaccurate results are produced by the ID model. The shape factor must be known within 20% of its true value for reasonably accurate results from the ID model with respect to stability. The 3D model does not offer any additional advantage in this regard unless the growth rates in the second and third dimensions differ more than 30%.