This paper examines the numerical simulation on dynamic fracture toughness values derived from SHPB testing programs with three-point bending specimens using RKR criterion. Three-dimensional and two-dimensional finite element analyses are performed by using software ABAQUS and 3D fracture mechanics code ZENCRACK. The finite element model includes the bullet, incident bar, specimen and supports. Three-point bending specimens with different ratios values of initial crack lengths to width are utilized for the simulations under the identical initial conditions. The fracture initiation time is explored with the RKR local stress fracture criterion. The dynamic fracture toughness value of the material is determined by the combination of response curve of the dynamic stress intensity factor and fracture initiation time. The experimental data are taken as a benchmark to verify the results of three-dimensional and two-dimensional finite element computations. It is found that the computational results from 3D finite element are more accurate.