The yielding phenomenon in the tensile curves of polymer fibres is explained by the onset of a sequential and plastic orientation mechanism of the chains brought abo ut by the resolved shear stress. The proposed simple theory shows that the yield strain in tension and compression varies from 0.5% for highly oriented fibres to about 2.2% for randomly oriented specimens, and that this range is the same for aliphatic polyamide, poly(ethylene terephthalate), cellulose II and poly(p-phenylene terephthalamide) fibres. In addition, the yielding mechanism explains the difference between the first loading tensile curve and the hysteresis curves of these fibres.