The commercial finite element package ABAQUS has been used to analyse the crack bridging process by Ti-15 at % V beta-phase particles dispersed in gamma-TiAl matrix in the presence of particle-matrix decohesion. Both the particle-matrix decohesion potential and the beta-phase materials constitutive relations are found to have a major effect on the ductility, fracture tough ness a nd failure mode of the beta-gamma two-phase material. The interface potential is found to primarily affect the distribution of the normal interface strength ahead of the advancing interfacial crack and the mode (gradual versus sudden) of decohesion. The beta-phase materials constitutive relations are found to influence the location of nucleation of the interfacial cracks and, in turn, the mode of decohesion. A metastable beta-phase that can plastically deform at low stress levels by undergoing a stress-assisted martensitic transformation, but experience a high rate of strain hardening is found to give rise to the largest levels of ductility and fracture toughness is the beta-gamma two-phase material.