This paper deals with the problem of the delamination of laminated beams. A model based on adhesion theory is adopted. The laminate is modeled as two beams in adhesion, with an initial defect in part of the interface. Adhesion is governed by two state variables: the relative displacement of the points belonging to the two beams and lying at the interface, and a damage parameter. This model is governed by a nonsmooth functional. Then, a simple regularized model is derived for the interface. The corresponding differential equations are given and the closed form solution is provided. Both the perfect nonsmooth and the regularized proposed models are used to study the classical double cantilever beam (DCB) specimen. In particular, a simple theory is developed to predict the external loads leading to delamination for pure mode I or pure mode II. Numerical computations, developed for both the nonsmooth and the smooth proposed models, are compared with results available in the literature.