Fracture behaviour of an infinite periodically layered composite body, with a Mode 3 crack parallel to the layering, is investigated. Upon deriving the Green function for a dislocation in a layered space, the problem is reduced to a singular integral equation of the first kind. The specific case of the bimaterial multilayered composite is considered in detail. The numerical results obtained for the stress intensity factor allows one to estimate the accuracy of the known approximate models with a reduced number of layers. It is found that for certain parameter combinations the stress intensity factor for the interface crack may exceed the corresponding value for a crack in a homogeneous space.