The problem on antiplane semi-infinite crack approaching to the elastic wedge-shaped inclusion is considered. The problem has been solved exactly using the Mellin integral transformation and the Wiener-Hopf method. The stress intensity factor of the crack tip KIII asymptotic behavior for short distances from the crack to the inclusion vicinity was studied. Depending on the composition parameters, the crack was shown to be stable (KIII → 0) or unstable (KIII → ∞). Providing that the interface has a corner point, the crack growth can be unstable (unlike the smooth interface) for some parameter values even though the crack approaches from the soft material to a relatively harder inclusion. Alternatively, the possibility of KIII → 0 exists provided the crack approaching from the hard material to a soft inclusion.