The two-dimensional boundary value problem on a nearly circular inclusion in an infinity elastic solid is solved. It is supposed that the uniform stress state takes place at infinity. Contact of the inclusion with the matrix satisfies to the ideal conditions of cohesion. To solve this problem, Muskhelishvili’s method of complex potentials is used. Following the boundary perturbation method, this potentials are sought in terms of power series in a small parameter. In each-order approximation, the problem is reduced to the solving
two independent Riemann – Hilbert’s boundary problems. It is constructed an algorithm for funding any-order approximation in terms of elementary functions. Based on the first-order
approximation numerical results for hoop stresses at the interface are presented under uniaxial tension at infinity.