We study high-temperature superconducting junctions of Josephson type. In manufacturing and functioning, measurement instrumentations of such type may undergo thermo-mechanical and electromagnetic effects of high intensity. As a result, the effective superconductive area of a sample may decreases compared with geometrical area; besides, data scattering can increase. We present some models of damage in high-temperature superconducting junctions of Josephson type. We consider devices of two types, SIS and SNS, where ‘S’ denotes a superconductor, ‘I’ denotes an insulator, and ‘N’ denotes a metal. Because there present interfaces, we consider appropriate models of damage and determine the parameters of strength and crack resistance. We present numerical results corresponding to various types of loading, geometry of interfaces, and particular models of damage. The models presented can be used for research and development of high-temperature superconducting composites.