When subjected to periodic loading, elastic systems containing contact interfaces might exhibit frictional slip which ceases after some loading cycles. In such cases, it is said that the system shakes down. For elastic discrete systems presenting complete contacts, it has been proved that Melan’s theorem, originally proposed for elastic-plastic problems, offers a sufficient condition for the system to shake down, provided that the contact is of an uncoupled type. In the present paper, the application of Melan’s theorem is speculated for systems involving plasticity and friction. A finite element example of an elastic-plastic solid containing a frictional crack is discussed.