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The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed atα=6° andσ=1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages: (1) the growth of the attached cavity sheet, (2) development of re-entrant flow and attached cavity sheet breakup, (3) attached cavity sheet rolling up and cavity cloud shedding, and (4) cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.