In order to analyze the mechanical properties of microcellular polyurethane elastic materials, the tensile and compression experiments were carried out. The experimental data was used to fit the classic hyperelastic constitutive models, and the parameters of the constitutive models were obtained . Through the error analysis, the applicability of constitutive models was discussed under different strain conditions. The fitted constitutive parameters were applied to simulate the static stiffness of WJ-8 fastner polyurethane elastic pad used for high speed railway, and the finite elemental simulation results were compared with the product test results, it showed that the relative errors between the tested values and the predicted values of Yeoh model, Van der Waals model and Ogden N=3 model were 8.44%，7.83% and 5.93% respectively, and the Ogden N=3 model had higher prediction accuracy than other models.