Nowadays, bonded joints have increasingly become the most used joining process in many industrial fields and even in civil engineering due to their simple geometry and structural efficiency and especially with the development of structural adhesives. Several solutions have been proposed in order to improve the mechanical strength of bonded joints by taking into consideration modifications to the adhesive edges and adherends to attenuate as much as possible the high stress concentration at the level of the adhesive. In this study, a 3D numerical model was developed in Abaqus to evaluate the influence of geometric changes in the adherends’ and adhesive edges on the mechanical strength of a single-lap joint under uniaxial tensile stress. Two modified geometric configurations of the bonded joint were proposed, taking into account on the one hand the presence of an adhesive fillet as the first modification and on the other hand, a removal of material at the level of the free edges of the adherends (adherends notching) as the second modification. The objective is to analyze the impact of these geometric modifications on the reduction of stress concentration in the adhesive and to explore how this new joint design can contribute to improve the strength of bonded joints. The results clearly show that a geometric modification at the level of the two free edges of the two substrates improves the strength of the joint and reduces the high stress concentrations in the adhesive. The joint strength is greatly improved if these modifications are optimized in relation to the overlap length and especially in relation to the thickness of the adherends and the adhesive. Adherend notching or applying an adhesive fillet resulted in a considerable reduction in peel stresses.