Herein, we present a numerical study on the deformation dependent behavior of magnetorheological elastomers with structured and unstructured particle distributions. To this end, finite element simulations are performed in order to calculate the effective magnetization and macroscopic actuation stresses for different specimens with realistic microstructures and varying mechanical preloads. Since the proposed microscale model is based on a continuum formulation of the magnetomechanical boundary value problem, the local magnetic and mechanical fields are resolved explicitly within the microstructures. The consideration of finite strains results in a finite element implementation of the coupled field problem for which a consistent linearization scheme is presented. In order to provide a better understanding of the deformation dependent behavior in real specimens, a study on chain-like structures is performed. It reveals that the interaction of the constituents in chain-like structures yields different material responses depending on their position. These findings are used to explain the influence of mechanical preloads on the behavior of samples with structured and unstructured arrangements of the particles. All of our results are in good agreement with experimental investigations which have been carried out for magnetorheological elastomers comprising a structured particle distribution.