The present paper deals with the constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10^<-3> to 800/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves within a strain range of nearly 8% for four different commercially available extruded polymers are determined on the standard split Hopkinson pressure bar. The low and intermediate strain-rates compressive stress-strain curves are measured in an Instron testing machine. The three parameters for the modified Ramberg-Osgood equation are determined by fitting to the data points on the plastic strain-stress curve using a least squares fit. The compressive stress-strain curves at three different strain rates derived from the modified Ramberg-Osgood models are compared with the experimental results. The limitations of the modified Ramberg-Osgood models are discussed. It is shown that the compressive stress-strain curves up to the maximum stress can be successfully predicted by the modified Ramberg-Osgood equation.