Shape memory polymers (SMP) are class of smart materials that can return from a deformed state (temporary shape) to their original shape (permanent shape) by applying an external stimulus (trigger), such as temperature. In this work, dynamic characterization of SMP and Epoxy samples is carried out using compressive Split Hopkinson Pressure Bar (SHPB) at different strain rates at room temperature. Here, Maraging steel rods of 16 mm diameter were used as the incident and transmitted bar in the SHPB. Cylindrical samples of higher diameter (> 10 mm) were used so that the impedance mismatch between the steel bars and the polymer samples is minimized. The tests were carried out in the strain rate range of 1000–9000/s. A 200 mm striker was used and the samples were tested without using pulse shapers. Both the SMP and Epoxy samples were prepared in house. It was found from the high strain rate tests that both epoxy and SMP samples were highly strain rate dependent. The compression test results on both epoxy and SMP specimens at same rate of loading have shown that the strain capability of the epoxy is limited to around 0.13 and internal cracks developed. However, SMP has deformed viscoelastically and responded to the load without a visible failure till 50% strain under dynamic compression. The present study is focussed to characterize the polymer composites high strain rate characteristics, further to develop the impact resistant composite structure for future applications.