This study investigates the stress wave propagation in adhesively bonded functionally graded (FG) circular cylinders subjected to an axial impulsive load. The volume fractions of the two constituent phases were assumed to vary according to a power law. The material properties of both upper and lower adherends, which are made of aluminum (Al) and silicon carbide (SiC) along the thickness direction, were calculated using the Mori-Tanaka homogenization scheme. The material composition was varied from the top ceramic to bottom metal layer (CM) for the upper adherend and metal to ceramic (MC) for the lower adherend. An epoxy-based adhesive was used to bond upper and lower adherends. The governing equations of the wave propagation in the adhesively bonded FG circular cylinder were discretized using the finite difference method. The distributions of the displacement and stress components at different times showed that the compositional gradient played a major important role on the displacement and stress levels as well as the wave speeds, whereas its influence on the displacement and stress profiles was minor. The axial displacement w(r,z) and axial stress sigma(zz)(r, z) components were found to be dominant displacement and stress components. The variations in the displacement and stress components vs. the time at the critical points of the adherend and adhesive layer indicated that the wave traveled at a slightly higher speed through the adherend with a stiffer (ceramic-rich) composition. Furthermore, the lower adherend underwent lower displacement and stress levels than those in the upper adherend since the adhesive layer behaved as a barrier to the stress wave propagation.