The article presents a numerical simulation of the mechanical properties of a Ti-Nb β-alloy on three different scales. The ab-initio approach is used to estimate the concentrations of the Ti alloy with required elastic properties. On the basis of molecular dynamics simulation, we calculate the adhesive force between individual particles of the alloy. The calculated dependence is implemented within the movable cellular automata method to determine the mechanical properties of Ti-Nb depending on the interparticle free space.