Elastic behaviour of Ti-6Al-4V alloy elaborated through additive manufacturing process is studied both experimentally and trough atomistic simulation. By studying rough samples after fabrication and after heat treatment, the elastic properties of the α' martensitic phase is compared to that of α + β microstructure. Atomistic calculations were also performed on various super-cells varying their chemical composition in order to simulate α and α' phases and their full elastic stiffness tensors were determined. Both experimental and simulation results show that Young modulus of the α' phase is lower than that of α phase, while it presents a more anisotropic behaviour.