Structures consisting of single or more materials, such as adhesive joints, may undergo large displacements and rotations under reasonably high loads, although all materials are still elastic. The linear elasticity theory cannot predict correctly the deformation and stress states of these structures, since it ignores the squares and products of partial derivatives of the displacement components with respect to the material coordinates. When these derivatives are not small, these terms result in a non-linear effect called geometrical non-linearity. In this study, the geometrically non-linear stress analysis of an adhesively bonded T-joint with double support was carried out using the incremental finite element method. Different T-joint configurations bonded to a rigid base and to a flexible base were considered. For each configuration, linear and geometrically non-linear stress analyses of the T-joint were carried out and their results were compared for different horizontal and vertical plate end conditions. The geometrically non-linear analysis showed that the large displacements had a considerable effect on the deformation and stress states of both adherends and the adhesive layer. High stress concentrations were observed around the adhesive free ends and the peak adhesive stresses occurred inside the adhesive fillets. The adherend regions corresponding to the free ends of the adhesive-plate interfaces also experienced stress concentrations. In addition, the effects of the support length on the peak adhesive and adherend stresses were investigated; increasing the support length had a considerable effect in reducing the peak adhesive and adherend stresses.