The existing analytical solutions for the peeling and shearing stresses in polymeric adhesively bonded structures are either too inaccurate or too complex for adoption by practicing engineers. This manuscript presents a closed-form solution that is reasonably accurate yet simple and concise enough to be adopted by practicing engineers for design analysis and exploration. Analysis of these concise solutions have yielded insightful design guidelines: (i) the magnitude of peeling stress is generally higher than that of shearing stress; (ii) the peeling stress in a balanced structure may be reduced most effectively by reducing the elastic modulus of the adherends or by increasing the adhesive-to-adherend thickness ratio and less effectively by reducing the elastic modulus of the adhesive; and (iii) the peeling stress in an unbalanced structure may be reduced by increasing the in-plane compliance of the structure, which may be implemented most effectively by reducing the thicknesses of the adherends and less effectively by reducing the elastic modulus of the adherends.