The generation and propagation of shock waves are important sources of cavitation instability and material damage. This paper describes an evaluation of the predictive ability of different turbulence models in a compressible cavitation flow for shock wave propagation. The Schnerr–Sauer cavitation model is used to model cavitation and the volume of fluid method is used to capture the water/vapor interface. The pressure pulsations and cavity evolution given by numerical simulations and experimental results are compared to evaluate the correctness of the numerical method and the prediction accuracy of different turbulence models. The propagation mechanism of the shock wave, the evolution of vortex structures, and the temporal and spatial distribution characteristics of the cavitating flow are analyzed. The results show that the results predicted by the large-eddy simulation (LES) model are in good agreement with the experimental results. The shock wave is caused by a pressure wave that is generated by the collapse of the previously detached cloud cavity. This pressure wave hits the trailing edge of the cavity, thus inhibiting the development of the cavity and delaying the period of the cavity. In the process of shock wave propagation, the peak pressure and the peak lift (drag) coefficient appear at the same time. The propagation of the shock wave strongly disturbs the motion of the vortices, causing the large-scale vortex structure on the trailing edge of the hydrofoil to be depressed and the stable vortex on the hydrofoil to lift. The vortex stretching term and vortex dilatation term dominate the transmission process of the eddy current, and the vortex dilatation term is the most important in the process of shock wave propagation. The pressure fluctuations in the evolution of the cavity lead to changes in the statistical structure of the velocity field. Moreover, the anisotropy of velocity fluctuations in the cloud-cavity region is higher than that in the region of the sheet cavity. The Reynolds-averaged Navier–Stokes (RANS) model underestimates the cavity volume and the pulsation characteristics of the flow field, and cannot capture the negative X-direction velocity and vortex structure changes in the shock wave propagation process. Moreover, the RANS model and detached-eddy simulation (DES) model cannot accurately predict the characteristics of the flow field near the wall, and overestimate the dominant frequency of the cavity oscillations. The LES model is better at capturing the flow field characteristics in unsteady dynamics, and reproduces the shock wave propagation process well.