The electronic mechanism behind the brittle fracture of trialuminide alloys is investigated using the full-potential linearized augmented plane-wave (FLAPW) total-energy method within the local density functional approach. To this end, the bulk phase stability, the elastic constants, the anti-phase boundary (APB) energy, the superlattice intrinsic stacking fault (SISF) energy, and the cleavage energy on different crystallographic planes have been determined. A small energy difference (=0.10 eV/unit formula) is found between the DO22 and L12 structures of Al3Ti. In general, the trialuminide alloys have large elastic modulus, small Poisson's ratio, and small shear modulus to bulk modulus ratio. An extremely high APB energy (=670 mJ/m2) on the (111) plane is found for Al3Sc, indicating that the separation between ½(110) partials of a (110)(111) superdislocation is small. Since the total superdislocation has to be nucleated essentially at the same time, a high critical stress factor for dislocation emission at the crack tip is suggested. The high APB energy on the (111) plane is attributed to the directional bonding of Sc(d-electron)-Al(p-electron). The same type of directional bonds is also found for Al3Ti. In addition, moderately high values of SISF energy (=265 mJ/m2) on the (111) plane and APB energy (=450 mJ/m2) on the (100) plane are found for Al3Sc. The brittle fracture of trialuminide alloys is attributed to the higher stacking fault energies and a lower cleavage strength compared to those of a ductile alloy (e.g., Ni3Al). While the (110) surface has the highest surface energy, the cleavage strength (=19 GPa) of Al3Sc is found to be essentially independent of the crystallographic planes. The directional Sc—Al bond becomes even stronger on the (110) surface, which may explain the preferred (110) type cleavage observed by experiment.