Using the micromechanics-based elastoplastic analysis method that has been formulated elsewhere, stresses to be produced at the cooling stage of hot-consolidated ceramic/metal "functionally gradient material (FGM)" plates are numerically analyzed with particular reference to composition-graded, ZrO2-Ni particulate composite laminates formed by hot-press diffusion bonding. The effect of in-plane and out-of-plane deformation constraints upon cooling is examined for plates with different patterns of compositional grading. The outermost ceramic layer suffers a very large tensile stress (far beyond its fracture-initiation level) upon cooling irrespective of the grading patterns if and only if both of these constraints are imposed. Residual thermal stress in the ceramic layer after removal of the constraints becomes tensile or compressive, depending on the grading patterns. A beneficial effect of the compressive residual stress in cyclic heat exposure of FGM plates is demonstrated.