In this paper the following problem is considered: find such loading on the path of boundary $\Gamma$ of the body $\Omega$, as near as possible to the desired value $F_\partial$, such that some linear transformation of the displacement field $u$ take desired value $h$ in a certain Hilbert space. The existence result of the optimal loading is given as in [4]. The weak formulation of the problem is in the form of variational inequality because of subdifferential form of the constitutive law in considered system. The existence result of the variational inequality is given as in [3].