An interaction of the semi-infinite crack of mode III with circular uncoated/coated inclusion is examined. As a result the use of the generalized integral transform of Mellin in the problem for the uncoated inclusion an exact analytical solution in the locked form is obtained. With the presence of coating the problem is brought to the solution of two integral Fredholm equations of second kind relative to displacements on the interfaces. The dependence of the stress intensity factor from the elastic modules of composition is studied.