An elastic finite element method numerical model developed for predicting thermal residual stresses in graded ceramic-ceramic materials has been applied to determine interface conditions favorable for achieving residual stress reductions. Using the Si3N4-BN FGM composite sintered in a heat-pressed sintering furnace as a model system, and for fixed specimen geometry, a study was performed to investigate the effects of different composition profiles on stress distributions established during the uniform cooling from an assumed sintering temperature. For each interface condition, the magnitude of specific stress components important for controlling interface failure are compared with each other. For the geometry and sintering condition, stress was reduced by nonlinear composition profiles.