The static and dynamic compressions of closed-cell ethylene-vinyl acetate (EVA) foams with different densities were conducted under various strain rates. The stress-strain curves were processed to determine the corresponding curves of energy absorption per unit volume and energy absorption efficiency, and energy absorption diagrams were produced. The influences of density and strain rate on the elastic modulus, yield strength, energy absorption per unit volume, optimal strain, densification strain, and energy absorption diagrams were analyzed and discussed. The whole stress-strain curve can be fitted with the Rusch formula. The strain rate does not change the shape of stress-strain curve, and has little influence on the elastic modulus. There exists the optimal density of EVA foam corresponding to its maximum energy absorption efficiency. Under a fixed strain rate, the optical energy absorption per unit volume is proportional to the optical stress on the envelope line in the energy absorption diagrams of EVA foams with different densities. The change in strain rate leads to the envelope line in the energy absorption diagrams of EVA foams with a given density having the larger slope and a negative intercept where the optical energy absorption per unit volume relies linearly on the optical stress. The empirical formulas of elastic modulus, yield strength, optimal strain, and envelope lines and their slopes are derived from the tested results.