Tube cold drawing processes are used to reduce tube diameters and thicknesses, while pulling them through a conical converging die with or without inner plug. An accurate modelling of the material deformation, friction behaviour and thermal effects is required in order to well describe these processes. Finite element (FE) modelling has already been applied to wire drawing as well as tube drawing [1, 2, 3]. All of these works carry out mechanical studies but none of them justify the value of their friction coefficient. The aim of the present study is to model tube drawing with a thermomechanical finite element analysis. It deals with the cold hollow sinking (without inner plug) and the mandrel drawing of stainless steel 316LVM tubes of small diameters (typically from 1 to 10 mm). It details the method to obtain all required parameters. During the forming process, mechanical and thermal measurements are recorded. Load cells are placed between the die and the frame for the drawing force. A thermocouple is placed inside the tube and a pyrometer, fixed on the die exit, records the tube external temperature. When possible, simulation parameters are determined thanks to mechanical or thermal tests. The material properties implied in the process, such as the anisotropy and the rate-dependence are studied. Shear and tensile tests are performed to determine the 316 stainless steel mechanical behaviour and lead to apply an isotropic temperature-independent Johnson-Cook law. The emissivity and the convection of the tube are determined by thermal tests during experimental tests. An infrared camera placed in front of the shearing device is used to observe the temperature variation fields. As the strain rates are high and the experiments times are short, heat loss through conduction, convection, or radiation can be neglected in comparison to thermoplastic heating.