Molecular statics atomistic simulations of the Ti-15 at % V body-centred cubic (bcc) beta-phase-gamma-TiAl interface and gamma-gamma lamellar boundary decohesion processes have been carried out to determine the corresponding decohesion potentials. The potentials are subsequently related to the dislocation structure of the interface-boundary. Atom ic interactions have been represented using the appropriate embedded atom method (EAM) interatomic potential functions. The results obtained show that the decohesion potential functions are quite complex because they have to account for the instabilities that occur under some modes of interface decohesion and for the periodic character of the interfacial shear. Lastly, the use of decohesion potentials to derive constitutive relations for continuum-type interfacial elements and their implementation in the finite element method are presented.