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Asymptotic behaviour of the elastic solution in a vicinity of the interfacecrack tip lying at a nonideal interface is investigated. The interface is assumed to beessentially stiffer in comparison with the bonded elastic materials. Additionally,inhomogeneity of the interface material is taken into account. The simplest case of theMode III deformation is under consideration. It is shown that the main terms of asymptoticbehaviour are practically similar to those in the case of the ideal interface (but withdifferent SIFs in each materials). Moreover, for some special loading there is no differencebetween the models at all. However, in a general case, additional singular terms of stressescan appear for the stiff nonideal interface model.