When fluid flows at a certain speed over an open cavity, large pressure fluctuation is produced. This fluctuation acts as an acoustic source and induces the damage of the stored instrumentation or the structure. The physical phenomena of rectangular open cavities with lids are numerically investigated in this paper. Two-dimensional compressible Navier-Stokes equations are computed with high-order and high-resolution numerical schemes. The characteristics of cavity resonance and acoustic propagation are analyzed according to the geometric variation of lids existing on the edges of the cavity. The lids change the resonance frequency, sound pressure level, and directivity of acoustic propagation. This also induces the transition of cavity resonance mode. Cross-correlation analysis and the integral form of Rossiter’s equation are used to analyze the transition of Rossiter’s mode and explain the sudden change of resonance frequency. The present results provide further understanding of cavity resonance and the effects of lids geometry.