Present work describes the structural stability and mechanical properties of the B2, D019 and O phases of Ti2AlNb intermetallic using first principles density functional theory (DFT) within generalized gradient approximation (GGA). The equilibrium lattice constant values of the B2, D019 and O phases are in good agreement with the experimental data. Formation energy/atom of D019 and O phases are nearly close and significantly lower than that of the B2. Density of states also follow similar trend. The strong directional bonding between Ti–Nb atoms has been observed in O and D019 phases which is absent in B2. All the three phases satisfy stability criteria in terms of elastic constants and are associated with ductile behaviour based on G/B ratios. These phases reveal the presence of anisotropy however, the extent of anisotropy is very high for the B2 in comparison to those of the D019 and O phases.