An analytical approach used to determine stress within an adhesive layer due to curvature mismatch between flexible adherends is implemented in an optimization analysis. The basis of this analysis is the classical beam on elastic foundation approach, where the adherend is described as a flexible beam and the foundation represents the adhesive layer. In this analysis, the optimal shape of a rigid substrate, described by the curvature of the substrate, is found based on various optimal conditions. These conditions include (1) minimizing the tensile stress in the adhesive layer (referred to as the peel stress), (2) maximizing the compressive stress at the free end and (3) minimizing the stress in the adherend. To minimize the peel stress, there should be a smooth transition between regions of differing curvatures. To minimize the stress in the adherend, the initial curvature mismatch between the adherend and the substrate should be reduced. The optimization scheme is described and results for two non-dimensionalized examples, associated with relatively stiff and relatively compliant systems, are presented.