In this study the effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded single- and double-lap joints was investigated considering the material non-linear behaviour of both adhesive and adherends and the geometrical non-linearity. The damaged adhesive and adherend zones exceeding the specified ultimate strains were determined based on the modified von Mises criterion for adherends and the failure criterion, including the effects of the hydrostatic stress states for the epoxy adhesives proposed by Raghava and Cadell. The stiffness of each finite element in the damaged zones was reduced to a negligible value, thus not contributing to the overall stiffness of the adhesive joint. This simple method provides useful information on the initiation and propagation of damaged zones in both the adhesive layer and adherends. The damaged adhesive zones due to a tensile load were observed to initiate around the rounded adherend corners inside the adhesive fillets and to propagate first towards both the free surface of the adhesive fillet and across the adhesive layer, and later along the adherend-adhesive interface. The damaged adhesive zones initiate at the left free-end of the adhesive-upper adherend inter-face and at the right free-end of the adhesive-lower adherend interface and propagate along these interfaces in the large adhesive fillets. In the bending test, the damaged adhesive zones appeared only at the left free-end in tension of the adhesive-upper adherend interface for the large adhesive fillets, but around the lower adherend corner for the smaller adhesive fillets. Later, it propagated with a similar mechanism as in the tensile load. In a double-lap joint subjected to a tensile load, the damaged zone appeared around the upper adherend corner inside the right adhesive fillet in tension, and propagated first towards the free surface of the adhesive fillet and through the adhesive layer towards the adhesive-middle adherend interface, and later along this interface. For all loading conditions, increasing the adhesive fillet size caused the damaged zone initiation to occur at a larger load level. The SEM micrographs of fracture surfaces around the adhesive fillets showed that the damaged zones initiated around the adherend corner inside the adhesive fillet and propagated through the adhesive fillets.