A procedure for minimizing the elastic shear stress concentration in adhesive lap joints is presented. The proposed method is based upon tapering the adherends to achieve smooth stiffness transitions and uniform shear stresses. Both single and double lap splices are considered, but numerical examples are restricted to the case of double lap joints. Nonisotropic materials and nonoptimum design limitations, such as minimum and maximum thickness adherends, load-line eccentricity, and peel stresses are treated, and typical results are presented.