This paper discussed the nonlinear torque of the engagement of selectable one-way clutch, which causes shift impact in the transmission. Firstly, dynamic models including steady states and transient state were built on the basis of the second Newton's law. Secondly, the nonlinear torque of the engagement of the one-way clutch was calculated by explicit FEM method. Thirdly, the torque of the output shaft and rotational velocities of both the input and the output shaft were calculated under the excitation of the torque of the input shaft and impact generated by the quick engagement of the one-way clutch, which was obtained by explicit FEM method. Finally, tests on the engagement of the one-way clutch during shifts were carried out. The test results have shown that the torque peaks and the vibration frequencies on the output shaft are similar in different situations when the speed of input shaft is different. The simulation results are similar to the test results. This proves the method proposed is appropriate in the research of the dynamic characters of the transmission shifting by one-way clutches.