This study investigates initiation and propagation of damage zones in the composite plates of an adhesively bonded single lap joint under flexural loads at the mesoscale level based on Tsai-Wu and Hashin failure criteria. The damage zones were evaluated in the unidirectional composite plates with ply lay-ups 10, 10, ... , 10. The mechanical properties of each failed ply of the upper and lower plates were modified based on a set of material degradation rules. Due to stress concentrations along the free edges of the adhesive layer and in the corresponding zones of the lower and upper plates, the peak stresses appeared along the left free edge of the upper plate-adhesive interface. Both failure criteria showed that the damage initiated in the first ply of the upper plate interface to the adhesive layer and propagated through this ply along this adhesive free edge, and then expanded through the neighboring plies in a similar failure mechanism. Hashin failure criterion predicted that the matrix and delamination failure modes were dominant in the upper plate, and higher first ply-failure loads and joint failure loads decreased significantly with increased ply fibre angle for the Tsai Wu failure criterion. The SEM photographs of the adhesive fracture surfaces due to three- and four-point bending tests showed that the local failure initiated inside the adhesive fillet and propagated along the upper plate adhesive interface. In addition, the interfacial adhesive failure and the partial damage in the first ply of the upper plate appeared for the ply lay-ups between 10 and 10 whereas the upper plates with larger fiber angles failed through the matrix of the upper plate in the fiber direction and a triangular adhesive bonding region, which decreases with increasing fiber angle. The interfacial adhesive failure is more apparent along the left free edge of the upper plate adhesive interface whereas the damage propagation is observed through both the adhesive layer and all plies from the interface to the top of the upper plate. Both failure criteria could predict reasonably the initiation and propagation of the damage zones in the composite plates of the adhesive joints, whereas the first ply failure and joint failure loads were underestimated since the non-linear adhesive model, non-linear matrix shear behavior, and geometrical non-linearity were not taken into account in the present analysis.