The article is devoted to the study of the contact interaction of a prestressed ring stamp and a half-space (base) with initial (residual) stresses without taking friction forces into account. The problem is solved for the case of equal roots of the resolving equation. The study is presented in a general form for the theory of large initial (finite) deformations and two versions of the theory of small initial deformations in the framework of the linearized theory of elasticity for an arbitrary structure of the elastic potential.