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A closed-form solution for laminated wood and sandwich biocomposite panels assembled with non-rigid adhesives and subjected to edgewise loading is presented. The solution satisfies the equilibrium equations of the layers, the compatibility equations of stresses and strains at the interfaces and the boundary conditions. To investigate the effects of the finite values of bonding stiffness on the mechanical responses of the panels, numerical evaluations are conducted. The results obtained have shown that the adhesive stiffness has a strong effect on the panel mechanical response. Beyond a certain level of stiffness, the usual assumption of perfect bonding used in classical theories is acceptable. This could provide an answer to what constitutes perfect bonding in terms of the ratio of the inner layer stiffness to the bonding stiffness.