In this study, the stress and stiffness analyses of adhesively-bonded double-containment corner joints have been carried out using the finite element method. In these types of joints, the philosophy is to use a corner support with slots into which the similar or dissimilar plates are bonded so that critical areas of the bond are under compression. Since the support geometry affects the analysis and design of such joints, the effects of geometrical parameters of the support, such as the support length, slot depth, support thickness, and chamfer length, on the stress distribution of the joint, particularly in the free ends of the adhesive layer in which the peak stresses occurred, and on the joint stiffness, were investigated. It was assumed that the adhesive had linear-elastic properties. Since the actual adhesively-bonded joints have a fillet at the free ends of the adhesive layer, the joints having a fillet at the free end of the adhesive layer were considered throughout this study. On the basis of the stress and static stiffness analyses, the dimensions of the corner support relative to the plate thickness were given.