In this paper, mathematical simulations of elastomers moderate deformations are performed, and a comparative analysis is carried out. Software package MSC.Marc 2012 is utilized for the simulations based on Saint-Venant, Mooney — Rivlin, and Hencky hyperplastic material models. It is shown that the Seint-Venan model is not effective for large deformations of elastomers, when the Mooney — Rivlin and Hencky models provide good approximation of elastomers deformations up to 50 % of scale. Physical experiments and computer simulations of Duotan sample twisting are conducted. Results of simulation based on Mooney — Rivlin and Hencky models are in good agreement with experimental data while the Mooney — Rivlin model provides slightly better relationship between twisting moment and twist angle in comparison with the Hencky model. Results of Mooney — Rivlin and Hencky models simulations of stretching of polyurethane sheet sample with a cut are compared to corresponding experimental data. The initially linear cut gradually opens and transforms into an ellipse during the deformation process. Experiments reveal that maximal principal stress being initially on top of the cut shifts deep into the sample. However, numerical simulations show that the maximal principal stress is located on the boundary (point of the ellipse). Possible reasons of that divergence are discussed.