The failure of fibre bund l e s is an important engineering problem which has been examined in a number of different ways. Most analyses are based on characterizing failure by some probability which is related to fibre dimensions and flaw distributions [1-8]. However, one of the main problems in determining fibre bundle failure is in the scale-up from tractable numerical solutions for small numbers of fibres, to fibre bundles of a 'useful' size [2-6]. This paper demonstrates one method, based on renormalization group (RG) theory, which circumvents these problems. It will be shown that the failure of fibre bundles can be characterized byFa critical probability, which is derived from the distribution of flaws alone. Failure strains may then be calculated using a knowledge of fibre dimensions and number. The method is verified using the data of Chi et al. [8]. The renormalization group method is based on the principle of scale invariance: that the failure of a bundle of fibres is the same at whatever scale we care to choose [9, 10]. It has been argued that such scale invariance cannot apply to fibre bundles [9]. However, we maintain that the flaw behaviour is scale invariant for large numbers of flaws, and that it is this which allows us to apply renormalization techniques to fibre bundle failure. The validity of this conjecture is supported by the work of Newman and Gabrielov [11]. At first inspection, the method appears similar to the chain of bundles approach [1-5], however, it will become clear that, although the two methods are complementary, there are certain differences. The failure criterion is the probability of failure of the whole structure should local load sharing result in failure. The derivation herein presented is similar to that given by Turcotte [10]. The probability of failure of the fibres is represented by the Weibull distribution: