Thermally induced residual stresses in metal-matrix composites can be large enough to yield, and in some cases fail, the matrix material immediately surrounding the fiber. The focus of this research is to evaluate the effect of interfacial layers between the fiber and matrix on these residual stresses and, more specifically, to determine the optimum design of such discrete interfacial layers in order to reduce the damaging levels of residual stress. One outgrowth of this investigation is the development of a software package that can determine the optimum design of a fiber/interfacial layer/matrix model for a variety of user-specified conditions (parameters). The optimization algorithm adopted in this procedure utilizes the method of feasible directions and accepts any combination of design variables, constraints and objective functions. The analysis model consists of a generalized plane-strain concentric cylinder assemblage that can handle both elastic and elasto-plastic analysis. An arbitrary number of cylinders can be included in the model, each with independent material properties. The inelastic analysis is performed using the method of successive elastic solutions. As an example, the circumferential stress distribution corresponding to a -1425Β°F drop in temperature for a SiC/Ti-24Al-11Nb system is evaluated. Through optimization, it is possible to identify the coefficient of thermal expansion (CTE) of the interfacial layer which will minimize the matrix circumferential stress, while keeping the circumferential stress in the interfacial layer less than, say, 650.0 ksi. Utilizing this optimization algorithm, an interfacial layer having a CTE of 2.8 times that of the matrix is found to reduce the critical matrix stress from 46.7 to 23.2 ksi, while satisfying the prescribed interfacial layer stress constraint.