Stick-slip vibration is common in the oil well drilling process and is detrimental to down-hole equipment and drilling efficiency. In recent years, a new type of drilling technology, torsional impact drilling, has been developed to mitigate the stick-slip phenomena, particularly in the drilling of deep or abrasive formations. With this drilling technique, highfrequency torsional impacts are generated and applied to the drill bit, providing the drill bit with auxiliary energy. By mitigating or suppressing the stick-slip vibration, part of the energy wasted as a result of vibration can be regained. However, the effect of these impact loads on the dynamic response of a drill string in a stick state is unknown. In order to address this issue, a continuous system model of a drill string that includes torsional impact load was constructed. In the model, a Fourier series approach was used for the impact load, and the mechanical model was resolved with the mode superposition method. Case studies were done to understand the drill string dynamics, with and without the impact. The case study results demonstrate that high-frequency torsional impacts have little influence on the dynamic response of a drill string in a stick state.