A formulation is presented which accounts for configurations of debonding patched cylindrical panels for which the edge of the debonded segment of the patch maintains sliding contact with the corresponding base structure. The formulation is incorporated with that which accounts for configurations for which a contact zone is present and for which no contact between the debonded segments of the patch and base structure occurs during debonding. Analyses are performed for two types of loading conditions: Applied circumferential tension and applied internal pressure. Results of numerical simulations based on analytical solutions of the problems of interest are presented in the form of threshold and stiffness degradation curves for specific structures with various geometries, material properties and support conditions, and reveal characteristic behavior of the evolving composite structure. In particular, the effects of edge contact on the debonding scenarios of the evolving structure are elucidated.