Numerical experiments were carried out on the high speed driven cavity flows in 2D curved channels to investigate mainly the pressure field. A density-based algorithm in ANSYS Fluent 13.0 was used in the present URANS simulations. The SST k-omega model was used for modeling the turbulence within an unstructured mesh solver. Validation of the numerical code was accomplished, and the results showed a good agreement between the numerical simulation and experimental data. Three channels (straight, concave and convex) with a nominal height of H = 4 x 10(-3) m under the transonic flow conditions were considered in the study. The cavity studied is L = 12 x 10(-3) m long with the depth ranging from D = 12 x 10(-3) m to 48 x 10(-3) m to obtain the length-to-depth ratios of L/D=1 to 1/4. The study comprised the analysis of the cavity surface pressures and the associated flow structures. The channel configuration influenced the cavity flowfield, and that influence finally resulted in a change in the surface pressure fluctuations in the cavity. The deep cavity attenuated the flowfield oscillation inside the cavity.