In this study, the stress and stiffness analyses of tee joints with double support were carried out using the finite element method. It was assumed that the adhesive had linear elastic properties and the presence of the adhesive fillets at the adhesive free ends was taken into account. The tee joints were analysed for two boundary conditions: a rigid base and a flexible base. In addition, each boundary condition was analysed for three loading conditions: tensile, compressive and side loadings. The stress analysis showed that the side loading resulted in the highest stress levels in the joint and in the adhesive layer for both boundary conditions. Since the joint failure is expected to initiate in the adhesive regions subject to high stress concentrations, the peak adhesive stresses were evaluated at these critical regions. In case of the rigid base, the peak adhesive stresses occurred around the left and right bottom corners of vertical plate for tensile and compressive loadings and at the left vertical adhesive fillet for the side loading. However, in case of the flexible base, the peak adhesive stresses occurred at the left bottom fillet for tensile and compressive loadings and at the left vertical fillet for the side loading. Whereas the peak adhesive stresses in the case of the flexible base were nearly ten times higher than in the case of the rigid base for the tensile and compressive loadings, they had rather close values for the side loading. In addition, the stresses at the critical regions showed a non-linear variation across the adhesive layer for all loading and boundary conditions. The effects of horizontal and vertical support lengths on the peak adhesive stresses and on the joint stiffness were also investigated and the support dimensions relative to the plate thickness were given based on the stress and stiffness analyses.