We simulate spontaneous dynamic propagation of rupture across two adjacent fault segments, subject to a triaxial compressive stress regime. These segments have different orientations and hence different focal mechanisms (vertical strike-slip and dipping thrust). Numerical simulations, using a BIEM (boundary integral equation method), have revealed that, under a typical triaxial homogeneous compressive stress regime where the magnitude of the intermediate principal stress lies halfway between those of the maximum and minimum ones, ruptures of different focal mechanisms are not likely to occur simultaneously in a single rupture event. Propagation of rupture from a vertical strike-slip fault segment to a pure dip-slip (normal/reverse) fault segment is possible only when the stress field is close to uniaxial compression, or when the intermediate stress magnitude is close either to the minimum or the maximum one. These findings are useful for evaluating possible earthquake scenarios along fault systems with complex 3D geometries.