Abstract: According to viscoplastic consistency model and the dynamic experimental results of concrete, a Drucker-Prager consistent rate-dependent model is set up. It evolves from the classical Drucker-Prager model by incorporating the effect of strain rate on concrete. Compared with experiment results, the model can predict the dynamic behavior of concrete accurately. A plane beam is studied using the model. The results are compared with those of the linear elastic model and rate-independent plastic model. The comparison shows that the dynamic behavior of the beam exhibits significant change when the effect of strain rate is considered.