1. A mathematical model of wire drawing speed was constructed, with allowance for inertial terms and the angle of taper, from the theory of viscoplastic flow. The stresses and temperature inside the deformation zone were determined. 2. The model makes it possible to find the critical drawing speeds corresponding to brittle and ductile fracture of the wire. 3. It was shown that the small-diameter range corresponds to ductile fracture, while the large-diameter range corresponds to brittle fracture. These findings agree with the experimental data in [1]. 4. The thermophysical and mechanical parameters of the material are generally nonlinear functions of the strain rate and temperature [8], so that the relation for critical drawing speed is more complicated.