Concrete is a typical kind of rate sensitive material. In this paper, the concrete specimens were tested in the SHPB experiment system. Based on H-J-C constitutive model, the SHPB experiment was simulated by LS-DANY. The stress-strain curves which were gat from numerical simulation in the LS-DANY were compared with the stress-strain curves which were gat from SHPB. The results showed that the H-J-C constitutive could simulate the dynamic characteristics of concrete both under room temperature. The result also showed that the concrete was strain rate sensitive. Based on the numerical simulation, the stress wave in the SHPB system was studied. The research of the numerical simulation showed that the stress waves tended to become stable after several oscillations in the incident bar. At the same time, stress wave of elements in r=0 (The distance of elements to the axis was 0) were bigger than the stress wave of r=0.5R (The distance to the axis was 0.5R) and r=R (The distance to the axis was R).