This paper is concerned with the computation of the effective elastic properties of periodic beam-like structures. The homogenization theory is used and leads to an equivalent anisotropic Navier-Bernoulli-Saint-Venant beam. The overall behavior is obtained from the solution of basic cell problems posed on the three-dimensional period of the structure and solved using three-dimensional finite element implementation. This procedure is first applied to two corrugated zigzag and sinus beams subjected to in-plane loading. Next, the axial elastic properties of a stranded '6 + 1' wire-cable are computed. The effective properties values obtained appear to be very close to analytical reference results showing the efficiency of the approach.