The expanded polystyrene foam is widely used as a protective material in engineering applications where energy absorption is critical for the reduction of harmful dynamic loads. However, to design reliable protective components, it is necessary to predict its nonlinear stress response with a good approximation, which makes it possible to know from the engineering design analysis the amount of energy that a product may absorb. In this work, the hyperfoam constitutive material model was used in a finite element model to approximate the mechanical response of an expanded polystyrene foam of three different densities. Additionally, an experimental procedure was performed to obtain the response of the material at three loading rates. The experimental results show that higher densities at high loading rates allow better energy absorption in the expanded polystyrene. As for the energy dissipation, high dissipation is obtained at higher densities at low loading rates. In the numerical results, the proposed finite element model presented a good performance since root mean square error values below 9% were obtained around the experimental compressive stress/strain curves for all tested material densities. Also, the prediction of energy absorption with the proposed model was around a maximum error of 5% regarding the experimental results. Therefore, the prediction of energy absorption and the compressive stress response of expanded polystyrene foams can be studied using the proposed finite element model in combination with the hyperfoam material model.