A stochastic model is introduced for predicting the stress-strain curve of a woollen yarn under longitudinal extension. The important features of a woollen yarn that are included in this model are the distributions of fibre length, diameter and strength, the effect of fibre reversals, the variation in linear density and twist along the length of a yarn, the radial variation in fibre packing, and the non-uniform arrangement of fibres in any particular yarn cross-section. The key deformation mechanisms within the model include variation in the stress between and along individual fibres, fibre breakage, fibre slippage, non-uniform strain along the yarn, and twist flow within the extending yarn. It is shown that the model can predict with reasonable accuracy the tenacity of woollen yarns which are made from fibres with a wide range of properties, and which contain a wide range of twist levels.