The buckling behavior of a face layer debonded locally from the core of a sandwich panel is analyzed by considering a Euler beam on Winkler foundation with debonds subjected to in-plane compression. Exact closed form solutions of the buckling load and mode shape are obtained, and corresponding numerical results are given to illustrate the solution. Results indicate that the wrinkling wavelength of the perfectly bonded face layer can be used as an appropriate characteristic length for normalizing the debond length of a relatively long face layer. The effects of length and location of debonds and the end constraints of the face layer on the load carrying capacity are discussed. Interactive effects due to two debonds and the overlapping of debond faces are also studied. A master curve based on a classical solution is developed by employing the new normalization of the debond length. A modification to the usual Winkler foundation constants is made for an isotropic core, and it agrees very well with published results of a finite element analysis.