Drawing process of thin walled tubes used to fabricate catheters and stents for medical applications was studied. Medical use needs accurate dimensions and a smooth finish of the inner and outer surfaces. This paper deals with 316L stainless steel tubes which are manufactured by means of cold drawing with or without inner plug (mandrel drawing and hollow sinking, respectively). To improve the quality of the finish of the tubes, numerical modelling can be used. In this way, a thermomechanical study of the drawing process is proposed to determine experimentally the physical parameters. This study proposes to evaluate the different parameters of the constitutive equations, of the thermal and friction models using specific experimental tests or using an inverse analysis on the drawing process. These parameters are validated by analysing other tube drawings. Finally the importance of physical parameters fit on drawing limits is emphasised, using a Cockcroft-Latham failure criterion.