The article deals with the behaviour of a fatigue crack propagating across a bi-material interface. A stability criterion for the crack touching the bi-material interface, taking into account the residual stresses closing the crack faces is formulated. The linear elastic fracture mechanics is assumed to apply and the finite element method is used in the calculations. The criterion proposed is applied to determine the fatigue threshold stress for crack propagation across the interface. It is shown that the threshold values for crack propagation are influenced by the residual stresses closing the crack and by the specific combination of the elastic constants of the materials used. The results contribute to a better understanding of the failure of structures with bi-material interfaces (protective layers, composite materials, etc.).