This paper describes the development of crystallographic preferred orientations in a type AISI304L austenitic stainless steel as a function of increasing reductions in area achieved by drawing at room temperature.In order to investigate these crystallographic textures X-ray diffraction measurements were made on transverse and longitudinal sections of the drawn rods and results are expressed in terms of texture coefficients and inverse pole figures.The results have shown that the initial duplex + fibre texture of the rolled and solution annealed starting rod develops towards a single fibre preferred orientation along the fibre axis with increasing true drawing strain.The single fibre texture is consistent with the preferred orientations observed in low stacking fault energy face centered cubic polycrystalline metals and alloys and with the lack of dynamic recrystallization due to the low homologous temperature of deformation. Martensitic a phase was detected in the cold worked rods since the early stages of plastic deformation and was found to be strongly textured with a single fibre preferred orientation, typical of polycrystalline body centered cubic metals and alloys.