Dynamic tensile and compressive tests are carried out to investigate the effect of strain rates on the dynamic tensile and compressive behaviour of concrete. Results of tests indicate that the tensile and compressive strengths of concrete increase with the loading rate. The initial tangential modulus and the critical strain of concrete in tension are independent of strain rate but those in compression slightly increase with the strain rate. Poisson's ratio of concrete in both tension and compression is not obviously dependent of loading rate. The static Drucker-Prager model is modified to the consistency viscoplastic Drucker-Prager model by considering the effect of strain rate. The simulation results using the proposed model show that the present model can simulate the uniaxial dynamic tension and compression behaviour of concrete well. Finally, the dynamic responses of a concrete beam under impact loading are analysed to investigate the influence of strain rates on dynamic responses of concrete structures.