Since the discovery of superconducting materials with relatively high transition temperatures (Tc), there has been a considerable effort both to understand the reason for the high Tc and to improve the mechanical properties, (the latter has been a limiting factor for practical applications). The YBa2Cu3O7-δ (YBCO) compounds have received considerable attention because of their high Tc and high upper critical magnetic field [l–3]. Additions of silver have recently been shown to improve the mechanical properties (toughness and strength) of these compounds [4]. Furthermore, the addition of the Ag can improve the conductive path between grains of superconducting YBCO and possibly help reduce the “weak-link” effect [5]. Note that whereas the addition of a low-volume fraction of silver does not adversely affect the superconductivity the introduction of transition metals to YBCO can have a detrimental effect on the superconducting properties. Also, the addition of silver has a minimal affect on the stress free lattice spacing. During fabrication of YBCO/Ag composites, differential thermal expansion upon cooling can lead to potentially troublesome residual stresses. Since the Ag contracts more than the YBCO, good bonding between the ceramic and silver could lead [6] to tensile stresses in the silver and compressive stresses in the YBCO for relatively small percentages of Ag. These residual stresses could lead to premature failure of the composite, debonding of the YBCO and Ag, and/or microcracking, which will affect the flow of superconducting current and the life expectancy of components made from this material. An understanding of the nature and magnitude of these stresses will help improve the design of these composites.