Aiming at the inaccurate problem of the polynomial function fitting the dynamic impact curve of expanded polyethylene foam (EPE), a precise and concise mathematical model was constructed to solve this problem. The experiment applies hook function, double-exponential function and common quadratic and cubic function were selected to fit the experimental data through 8 fitting points. The fitting effects of the four mathematical models were compared and analyzed by changing the density and thickness of the experimental materials and the drop height of the experiment. The results show the fitting degree of both the double-exponential function and the hook function can reach above 0.98, and the fitting degree of quadratic and cubic function is lower than 0.9. In addition, the fitting effect of the polynomial function is unstable and the error is large at the lowest point of the fitting curve. Compared with the double-exponential function, the hook function has fewer parameters, and the fitting effect is similar, so it is easier to popularize in practical application.