Successful operations for plug and abandonment (P&A) must seal the well bores to ensure that there is never leakage between geological horizons penetrated by the wellbore or to the surface. Acoustic logging methods for cement bonding, being designed for material evaluation of a single casing string, are currently unable to characterize cement and bonding of cement to casing when multiple concentric casing strings are present. When this is the situation, the inner pipes of the wells must be removed to leave only one layer of steel and cement that can be evaluated which increases the cost of the P&A. With the goal of improving the reliability of acoustic logging methods for material bonding evaluation in multiple casing bonding conditions, we use a 3D Finite Difference (3DFD) method to simulate wave propagation in cased borehole models including single casing and dual casing boreholes with different bonding conditions. Pressure snapshots for different models are shown which allow us to better understand the wave propagation. Data processing methods such as velocity-time semblance and dispersion analysis facilitate the identification of propagation modes in the different models. A modal decomposition method is also used in the data with an eccentered source. For single casing models, we assume that the basic formation modes can be easily discerned when the casing is well bonded. The P wave is submerged in the casing mode and the S wave has poor coherency when the cement is replaced with fluid. Acoustic logging tool with a monopole sonic source can be used for determine the bonding condition of different interfaces for the single casing model. For the dual casing models, it is easy to determine if there is good cement in both annuli and whether the outer casing is fully bonded by using monopole logging data. However, if the first annulus is not bonded well, the monopole data are not useful but it may be possible to use dipole or higher order modes to distinguish the bonding condition. The modal decomposition method for the data with an eccentered source helps us understand the higher order modes. New data processing methods and tool designs can be developed when we have a full understanding of the wavefield excited by an eccentered source.