New electrostrictive lead magnesium niobate ceramics (PMN) are promising materials for applications in the field of actuators, transducers, and motors. These materials have strains roughly an order of magnitude larger than those of the lead zirconate--titanate (PZT) ceramics. However, the use of these electrostrictive materials for practical applications presents some difficulties: highly nonlinear properties, temperature dependence of dielectric permittivity near the dielectric maximum, dc bias field needed. To improve the use of these electrostrictive materials, a better knowledge of the physical tensors of PMN and the development of a numerical tool are necessary. In this study, the development of a two-dimensional electrostrictive element in the ATILA code for nonlinear static analysis and time-domain analysis is presented. Two different models are tested including or not the effect of polarization saturation. The validity of both models is demonstrated by comparing computed strain and charge density with analytical solutions and measured results for a PMN bar at various electric dc fields and mechanical prestresses. Measurements are realized to obtain the complete physical tensor of PMN. Finally, the model is applied to a Janus transducer to describe the application of prestress and the electrical dc polarization.