The work aims to establish EPE constitutive model and study EPE buffer coefficient-maximum stress curve according to the model. The EPE stress-strain curve was obtained by static compression test. The cubic Bezier curve was used to fit the experimental curve. According to the fitting curve, the cushioning coefficient was acquired, and then the buffer coefficient-maximum stress curve was obtained. The sectioned EPE constitutive models were obtained through fitting with cubic Bezier curve. Based on the constitutive models, the parametric equations of buffer coefficient-maximum stress curve in EPE sections were established. Both the constitutive models and the EPE buffer coefficient-maximum stress curves based on the constitutive models were converged to the subsection point (0.3, 0.1075). When the stress value fitted was 0.4529 MPa, the minimum value of the buffer coefficient was 5.0362. The stress-strain curve of EPE fitted by the cubic Bezier curve has good fitness with the experimental curve. The two EPE buffer coefficient-maximum stress curves based on the constitutive model and the experimental data have good fitness. It is feasible to study the EPE cushion characteristic curve based on the constitutive model fitted by cubic Bezier curve.