This study presents a numerical analysis of the effects of a rigid flat wall with oscillating motion on the pressure wave propagation during a single spherical cavitation bubble collapse at different initial bubble positions. Different nondimensional distances $S$ = 0.8, 0.9, 1.0, 1.1, 1.2 and 1.3 were considered to investigate the effects of initial in-phase and out-of-phase oscillations of the flat wall. Numerical simulations of cavitation bubble collapse near an oscillating wall were conducted using a compressible two-phase flow model. This model incorporated the Volume of Fluid (VOF) interface-sharpening technique on a general curvilinear moving grid. The numerical results were consistent with published experimental data. The simulation examined the impact of oscillating walls on bubble behavior and the resulting pressure peaks observed on the wall surface. The numerical results demonstrate the significant impact of wall oscillation conditions on bubble collapse and migration behavior, and consequently, the generation of pressure waves with significantly different propagation and pressure peaks induced by shock impact on the rigid wall. Different behaviors were observed in the trendlines of the pressure peaks and maximum jet velocity under in-phase and out-of-phase oscillating walls, with distinct values. At $S\ge 1.0$, a higher-pressure peak on the wall was observed in the case of the out-of-phase oscillating condition, whereas a higher-pressure peak was found in the case of the in-phase condition at $S<1.0$. The highest-pressure peak was found at $S=0.8$ in trend lines of in-phase and $S=1.1$ in trend lines of out-of-phase oscillation effects.