Abstract A detailed study on the inter-metallic alloy, Zr₂TiAl, has been carried out using first principle electronic structure calculations. We found that a small value of bi-axial strain/stress cause a phase change from anti-ferromagnetic(AFM) to ferromagnetic(FM) with a structural transition from face center cubic (fcc) to body center tetragonal (bct). Calculated electronic band structures show that all strained structures are metallic in nature with Zr-d and Ti-d orbital dominated energy bands near the Fermi level(E _F ). The stability of FM phase is confirmed with phonon dispersion calculations by using density functional perturbation theory (DFPT). It has been observed that AFM state with both positive and negative bi-axial stress exhibits unstable modes while corresponding FM state shows no such instability. This clearly indicates the existence of large spin phonon coupling in this material.