This study addresses the wave propagation in adhesively bonded similar and dissimilar circular cylinders under an axial impulsive load. The four configurations are considered such as adhesively bonded aluminum-aluminum (Al-Al), steel-steel (St-St), aluminum-steel (Al-St), and steel-aluminum (St-Al) joints. The governing equations of the wave propagation are partial differential equations which are not usually amenable for analytical solutions under complex boundary conditions. Therefore, they are solved numerically using the finite difference method for spatial and temporal discretization. Each component of the adhesively bonded circular cylinders exhibits completely different stress and deformation states under an axial impulsive load. The axial displacement [GRAPHICS] and axial stress [GRAPHICS] components were dominant in both upper and lower adherends as well as the adhesive layer. The peak displacement levels became maximal in the bonded Al-Al and Al-St joints, decreased slightly in the bonded St-Al joint, and became minimal in bonded St-St joint. As the adhesively bonded joint becomes stiffer due to a stiffer (St) upper adherend, the bonded St-St and St-Al joints experience higher stress waves in comparison with those in the bonded Al-Al and Al-St joints, respectively. Moreover, the wave travels at a slightly higher speed through the adherend with a stiffer (St) material.