Metalworking is an essential process for the manufacture of machinery and equipment components. The design of the die geometry is an essential aspect of metalworking, and directly affects the resultant product’s quality and cost. As a matter of fact, a comprehensive understanding of the die bearing geometry plays a vital role in the die design process. For the specific case of wire drawing, however, few efforts have been dedicated to the study of the geometry of the bearing zone. In this regard, the present paper involves an attempt to investigate the effects of different geometries of the die bearing. For different forms of reduction as well as bearing zones, measurements are carried out for the wire-drawing process. Subsequently, by extracting the friction coefficients from the electrolytic tough pitch copper wire in cold-drawn essays, the numerical simulations are also implemented. We present the results on both the superficial and center radial tensions obtained by finite element methods. It is observed that the reduction of the friction coefficient leads to an increase in radial stress, while for a given friction coefficient, the substitution of the C-type die by the R-type one results in a decrease in the superficial radial stress of up to 93.27%, but an increase at the center of the material. Moreover, the die angle is found to play a less significant role in the resultant center radial stress, but it significantly affects the superficial radial stress. Lastly, R-type dies result in smaller superficial radial stress, with a change of up to 34.48%, but a slightly larger center radial stress up to 6.55% for different die angles. The implications of the present findings are discussed.