The influence of thermal stress in joints, which is induced during cooling by the difference in thermal expansion coefficient between the joined brittle materials, on the failure probabilities of the joints was estimated. A numerical analysis by the finite-element method was carried out on SiC/Si<sub>3</sub>N<sub>4</sub> joints. It was assumed that the strength of each material obeys the Weibull distribution function and that the joining strength is high enough to prevent rupture at the joining interface. Since the tensile stress develops predominantly at the side of SiC which has a larger thermal expansion coefficient than that of Si<sub>3</sub>N<sub>4</sub>, the Weibull modulus of SiC was taken into consideration for calculating the failure probability of the joint. The dimension of the joint and the Weibull modulus of SiC member were shown to have great influence on the failure probability. Therefore, these two factors must be taken into consideration in addition to the fracture strength of material to be joined for the evaluation of the joining strength of various brittle materials.