The strength distribution of alumina single fibres has been evaluated at room temperature. It has been shown that the classical Weibull distribution function cannot account for the observed dispersions for different gauge lengths. New statistical descriptions have been developed, which take into account the fact that the fibre has an irregular cross-section. Rupture probability functions are derived for cases where the characteristic length for diameter variation is much smaller or much larger than the gauge length. The fibre has then to be viewed as a structure. The material constituting the structure was supposed to obey a simple Weibull law. The method requires the fit of the Weibull parameters of the fibre material and the determination of the geometrical characteristics of the fibres.