During cold wire drawing process, the drawing stress applied to the wire at the exit of the die must be lower than the material yield stress (including strain-hardening) to avoid wire necking and fracture. Several studies have been developed to investigate and model the stress acting on the wire in the single pass drawing and its dependence on the main process parameters. The aim of this work is to apply an analytical model for the calculation of the drawing stresses during the whole complex multi-pass manufacturing process in industrial environment, considering not only the forces acting in the die but also the driving forces of the rotating capstans (drawing tension and back tension). The drawing of ETP Pure Copper (99.9% in weight), using two industrial multi-pass machines with different reduction ratio sequences, is analysed and then discussed in order to understand the different failure rates. Finally, the study compared step by step, the evolution of the drawing stresses respect to material yield stress when different processing conditions (i.e. change of capstan windings, change of friction conditions in the die and in the capstan) are applied.