The failure properties of flax fibres were investigated using a tow behaviour-based approach that was developed on ceramic and glass fibres. The Weibull and normal strength distributions of filament failure strains and the true statistical parameters were extracted from the tensile curve of a tow test specimen made of several 100 of filaments. Tensile tests were carried out on flax tows possessing more than 1000 continuous elementary fibres. The force-strain curves were found to follow the theory of bundles of independent and parallel continuous filaments. Weibull and normal distributions of filaments failure strains were reproducible and in excellent agreement. The results of the present work are compared to strengths of elementary and technical fibres reported in the literature. The dependence of statistical parameters on factors including sample size and selection, and method of experimental data analysis was investigated. For this purpose, subsets of failure strains were analysed, and the normal distribution-based approach was applied to sets of failure strain data of elementary fibres reported in the literature. Finally, the flax fibre was compared to E glass fibre using statistical distributions of failure strengths.