Near-surface axial tensile residual stresses (from manufacturing) are reportedly detrimental to the yield strength of cold-drawn wires. Therefore, a reliable evaluation of their magnitude is necessary. The size and geometry of electrical wires can pose challenges for experimental measurement of those residual stresses. For that reason, the finite element analysis can prove useful. However, great care must be taken with the right choice of strain hardening law for a sound assessment of residual stresses. Given the complex loading condition during cold drawing, cyclic loading arises through the wire cross section even in single-pass drawing. As a result, it is of crucial importance to account for associated backstresses. The current study makes a comparison between two different hardening laws' prediction of axial residual stress profiles in numerically cold-drawn Cu-Al composite wires of various Al volume fractions. The impact of die geometry on this prediction was also examined for a 25%Al-wire. To that end, a combined isotropic-kinematic law and a pure isotropic constitutive equation were considered. The results imply a possible overestimation of residual stresses by the pure isotropic model at relatively low Al volume fractions. The difference between the maximum magnitudes of tensile or compressive residual stresses (predicted by the two models) could be as large as about 100 MPa (larger than the yield strength of the starting materials). Furthermore, the tooling geometry minimally affects the prediction of the hardening models. In conclusion, backstresses are not to be overlooked for accurate estimations of drawing residual stresses at low Al volume fractions.