The present work describes the structural and mechanical behaviour of three phases namely B2, D019 and O phases of Ti2AlZr intermetallic using first principles density functional theory (DFT) within generalized gradient approximation (GGA). The equilibrium lattice constant values of B2, D019 and O phases are in good agreement with the experimental and theoretical data, respectively. Formation energy of O phase is minimum followed by D019 and B2. Bonding characteristics of these phases have been explained based on electronic density of states and charge density. All the three phases satisfy the Born stability criteria in terms of elastic constants and are associated with ductile behaviour based on G/B ratios. The B2 phase exhibits very high anisotropy in comparison to those of the D019 and O.