Fatigue failure in polycrystalline materials occurs by initiation and propagation of fatigue cracks. Fatigue cracks can initiate transgranularly or intergranularly. While considerable progress has been achieved in the explanation of the mechanism of transgranular fatigue crack initiation intergranular initiation is still the subject of controversy. A recent study of the crack initiation in superaustenitic Sanicro 25 steel [1] revealed the important role of persistent slip markings (PSMs) in the grains adjoining the grain boundary. A novel mechanism of intergranular fatigue crack initiation has been proposed. Provided the cyclic slip cannot proceed from one grain to the neighbour one, extrusions and intrusions arise not only on the surface but also on the grain boundary. Growing intrusions represent void-like defects and growing intrusions push neighbour grain apart. A systematic study of intergranular cracking has been performed on polycrystalline copper cycled with high and low strain amplitudes. SEM observations of the early stages of fatigue crack initiation on the grain boundaries, EBSD study of grains orientation, FIB cutting of the grain boundaries and simultaneous documentation of the effect of extrusions and intrusions on the grain boundary cohesion are reported simultaneously with the conditions favourable for the initiation of the fatigue cracks.