A new modified Weibull distribution function has been suggested for analysing the strength of fibres used as reinforcements for advanced composites. The function provides an upper and a lower strength limit and is characterized by two shape and two location parameters. A method for determining the parameters of this distribution from the analysis of the tensile curves of fibre bundles has also been developed. Application of the method to the experimental results on Thornel-300 carbon fibres shows that the shape parameters become modified in the case of bundles.