To determine the level of residual stresses during wire drawing, the finite element method implemented in the ABAQUS software module was used. A comparison is made of the stress state of a piece of wire located on the output side of the die at the moment of drawing and after the wire leaves the die. Calculations have shown that all types of normal stresses in the center of the wire are negative, that is, they are compressive stresses. On the surface, the stresses during both drawing and unloading are tensile, with the exception of the radial stress equal to zero. The residual axial stresses after unloading are approximately halved, and the tangential stresses change insignificantly. The residual principal normal stresses are also determined.