This paper presents systematic numerical study of stresses in the adhesive of a single-lap joint with the objective to improve understanding of the main material and geometrical parameters determining performance of adhesive joints. For this purpose a 3D model as well as 2D model, optimized with respect to the computational efficiency by use of novel displacement coupling conditions able to correctly represent monoclinic materials (off-axis layers of composite laminates), are employed. The model accounts for non-linearity of materials (adherend and adhesive) as well as geometrical non-linearity. The parameters of geometry of the joint are normalized with respect to the dimensions of adhesive (e.g. thickness) thus making analysis of results more general and applicable to wide range of different joints. Optimal geometry of the single-lap joint allowing to separate edge effect from end effects is selected based on results of the parametric analysis by using peel and shear stress distributions in the adhesive layer as a criterion. Three different types of single lap joint with similar and dissimilar (hybrid) materials are considered in this study: a) metal-metal; b) composite-composite; c) composite-metal. In case of composite laminates, four lay-ups are evaluated: uni-directional ([08]T and [908]T) and quasi-isotropic laminates ([0/45/90/-45]S and [90/45/0/-45]S). The influence of the abovementioned parameters on peel and shear stress distributions in the adhesive layer is examined carefully and mechanical parameters governing the stress concentrations in the joint have been identified, this dependence can be described by simple but accurate fitting function. The effect of the used material model (linear vs non-linear) on results is also demonstrated.