Quantitative estimation of failure of a LiTaO3 single crystal due to thermal stress was investigated. Cylindrical test slabs were heated in a silicone oil bath, then subjected to large thermal stress by pouring silicone oil with room temperature. Cracking occurred during cooling. A transient heat conduction analysis was performed to obtain a temperature distribution in a test slab at the time of cracking, using the surface temperatures measured in the test. Then thermal stress was calculated using a temperature profile of the test slab obtained from the heat conduction analysis. It is found from the results of thermal stress analyses and the observation of the cracking in the test slabs that the cracking induced by thermal stress occurs mainly in the cleavage planes due to the stress component normal to the plane. As for a size effect of failure stress, large-sized cylindrical test slabs show lower failure stress than small-sized ones. Four-point bending tests were also performed to examine the relationship between the critical stress for cracking induced by thermal stress and the four-point bending strength. A useful relation was derived for predicting the critical stress for cracking induced by thermal stress from the four-point bending strength.