Abstract: The split Hopkinson pressure bar (SHPB) tests for concrete were numerically simulated by using the Holmquist-Johnson-Cook (HJC) constitutive model. The contact stiffness in the penalty function algorithm was reasonably determined. The stress-strain curves of the concrete specimens were reconstructed from the simulated results by applying the two-wave method used in the data processing of the SHPB tests. The effective ranges of the stress-strain curves obained in the SHPB tests and their mechanical regularity were analyzed. By comparing the stress-strain curve obtained from the SHPB test with the reconstructed curve from the numerical simulation, it can be found that the mechanical behaviors of the two curves are similar. It is verified that the HJC model is a reasonable constitutive model for describing the concrete materials. Numerical simulations were carried out for the SHPB tests of the concrete specimens with different tolerances in parallel. The simulated results show that the tolerances in parallel of specimens affect the SHPB tests much more remarkably than the stress(strain) nonuniformity in a certain strain-rate range.