Bolted joints have been widely used in engineering structures because of their advantages of simplicity, economy, and assembly. However, material nonlinearities, interface nonlinearities and uncertainties in the assembly process will lead to the dynamic response to become very complex. This work investigated the effect of assembly uncertainties on shock propagation through a bolted lap joint under impact loading. The object of the study was a bolted lap joint subjected to separate Hopkinson pressure bar (SHPB) test. First, a high-fidelity finite element model of the bolted lap joint was developed, and the model was validated by comparing with the experimental results. The error between simulation and experimental results prompted the necessary to consider the uncertainty effect. Then, the effects of multiple uncertainties were considered to identify important input random variables related to the impact response of the joint. The results showed that the slip between the connected parts has the most significant effect on energy dissipation and stress wave propagation. Finally, useful conclusions for the design of bolted joints were obtained from the computational results and discussions.