A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and an elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress functions. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. the local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.