We address the influence of individual fibre stress-strain non-linearity on the extraction of Weibull-parameters from fibre bundle tensile tests. We extend the statistical theory of fibre bundle strength to include the non-linear elastic behaviour observed in many technically important fibres, e.g. glass-, carbon-, and alumina-fibres. It is shown that neglecting this non-linearity may lead to significant errors in determining the shape and scale parameters of the fibre fracture strength Weibull-distribution. A refinement of the existing extraction technique, accounting for this effect, is presented. The error resulting from neglecting the non-linear behaviour is assessed through a parametric study of the Weibull parameters for different levels of non-linearity. Explicit calculations are performed for two fibres of technical importance, namely Nextel 610e a-alumina fibre and a T300 carbon fibre. q