This paper deals with the constitutive modeling of energy absorbing foams. Two mechanical-analog hyper-elastoplastic models are constructed for simulating the characteristics of semi-rigid and rigid foams. These piecewise linear models are suitable for describing the loading as well as the unloading behavior of material. The result from quasi-static compression tests are used to determine the three parameters of the models. It is observed that the models can be used in the prediction of stress-strain behavior as well as the energy absorption characteristics.