Tooth tissues and many of the dental restorative materials, e.g. ceramics and resin composites, are brittle in nature. It is typical of these materials to show a large variation in their fracture strength. A mechanistic approach which can account for their complex shapes and stress distributions is needed in the design and performance optimization of dental restorations. Thus, this chapter introduces the use of the Weakest-Link Theory, in conjunction with the Weibull function, to predict the failure probability of brittle structures and to analyse and design against failure of dental restorations.