EVA foams, like all other polymers, also exhibit strain-rate effects and hysteresis. However, currently available approaches for predicting the mechanical response of polymeric foam subjected to an arbitrarily imposed loading history and strain-rate effect are highly limited. Especially, the strain rates in the intermediate rate domain (between 100 and 102 s–1) are extremely difficult to study. The use of data generated through the drop tower technique for implementation in constitutive equations or numerical models has not been considered in past studies. In this study, an experiment including a quasi-static compression test and drop impact tests with a high speed camera was conducted. An inverse analysis technique combined with a finite element model for material parameter identification was developed to determine the stress–strain behavior of foam at different specific strain rates. It was used in this study to simulate multiple loading and unloading cycles on foam specimens, and the results were compared with experimental measurements.