In this paper we have considered an antiplane problem for elastic piecewise homogeneous half-space, consisting of two qwarters of space with different elastic properties, strengthened in its boundary by semi-infinite piecewise homogeneous rather thin cover-plate passing the boundary of heterogeneity. It has been thought that elastic half-space deforms under the action of concentrative forces applied correspondingly to the part boundary of the half-space. For determination of the unknown tangential stresses, acting in the section of fixing the half-space and cover-plate with the help of Mellin’s transform and factorization method the problem is brought to Fredholm integral equation of second kind, which is solved by means of successive approximation method.