We used density-functional theory to assess the electronic structure, elastic properties and planar fault energies of the B2 Ti(AlxNb1-x) (0.2 <= x <= 0.8) phase in relation to the composition and chemical ordering. We found that the covalent bonding becomes stronger for B2 Ti(AlxNb1-x) with higher Al concentration and long range order (LRO) parameter. Based on a universal ductile-to-brittle criterion by integrating Pettifor's Cauchy pressure with Pugh's modulus ratio, the deformability becomes less for Ti(AlxNb1-x) with higher Al concentration and LRO parameter, which is well correlated with the bonding character. Rice's ratio has an anti-correlation with Pugh's modulus ratio for Ti(AlxNb1-x). According to Rice's criterion, Ti(AlxNb1-x) with various Al concentration and LRO parameter are brittle in pure mode I loading, however, Nb-enriched disordered and low-ordered Ti(AlxNb1-x) may satisfy Rice's criterion for nucleation of dislocation and thus, are ductile in mode II or III loading. The hardness increases but the fracture toughness decreases obviously with increasing the degree of covalent bonding in Ti(AlxNb1-x).