The scope of this work is the determination of single-crystals elastic constants (SEC) from X-ray diffraction lattice strains measurements performed on multi-phase polycrystals submitted to mechanical load through a bending device. An explicit three scales inverse self-consistent model is developed in order to express the SEC of a cubic phase, embedded in a multi-phase polycrystal, as a function of its X-ray Elasticity Constants. Finally, it is applied to a two-phases (α+β) titanium based alloy (Ti-17), in order to estimate Ti-17 β-phase unknown SEC. The purpose of the present work is to account the proper microstructure of the material. In particular, the morphologic texture of Ti-17 a-phase, i.e. the relative disorientation of the needle-shaped grains constituting this phase, is considered owing to the so-called Generalized Self-Consistent model.