The work aims to improve Sherwood-Frost constitutive model and improve the simulation accuracy of EPE impact with high speed and large deformation. Static compression tests were carried out on EPE with a universal material testing machine to obtain stress-strain curves at different compression rates. The strain rate terms of Sherwood-Frost constitutive model were improved by combining Seeger model of thermal activation mechanism with inverse proportional function model, and the reliability of the model was verified by experiments. The Sheerwood-Frost constitutive model was used to simulate the impact of EPE materials on the ABAQUS software, and the accuracy of the simulation was verified by the test data. The improved constitutive model was in good agreement with the experimental data, and the maximum acceleration errors were 6% and 2.03% respectively at the impact height of 1200 mm and 1300 mm. The improved Sherwood-Frost constitutive model has good reliability, and the impact simulation of EPE with high speed and large deformation based on the model has good accuracy.