Spiral strands subjected to tensile force and bending loading display a nonlinear dissipative behavior due to frictional interactions between their elementary wires. This study aims to provide an efficient method, based on a computational homogenization procedure, to accurately characterize the nonlinear response of such strands. By using 1D beam elements in both micro- and macro-scale, homogenization is performed along the axial direction of a representative volume element (RVE), leading to expressing a boundary value problem on RVE, driven in a mixed manner by either strains or resulting forces or moments. The boundary value problem on the RVE is solved using an in–house implicit finite element solver for finite strain, considering all frictional contact interactions. A method is proposed to predict the bending moment’s evolution for any curvature variation from the simulation results of only one bending loading test on the RVE. The nonlinear behavior of the strand in the micro-scale identified through this offline technique can then be used in the macro-model to simulate various bending loading tests under constant tensile load. Results obtained with the multiscale model are compared to those provided by direct numerical simulation to demonstrate the validity of the proposed approach