Experiments of crack propagation in rubbers have shown that a discontinuous jump of crack propagation velocity can occur as energy release rate increases, which is known as the "mode transition" phenomenon. Although it is believed that the mode transition is strongly related to the mechanical properties, the nature of the mode transition had not been revealed. In this study, dynamic crack propagation on an elastomer was investigated using the finite element method (FEM) with a hyperviscoelastic material model. A series of pure shear test was carried out numerically with FEM simulations and crack velocities were measured under various values of tensile strain. As a result, our FEM simulations successfully reproduced the mode transition. The success of realising the mode transition phenomenon by a simple FEM model, which was achieved for the first time ever, helped to explain that the phenomenon occurs owing to a characteristic non-monotonic temporal development of principal stress near the crack tip.