The authors propose a mathematical model for deformable elastic mechanical systems which describes the formation of a near-surface inhomogeneity due to both the process of local mass displacement and the dissipative processes. In this framework, a problem of stationary stress-strain state of an infinite hollow cylinder is solved. It is shown that the near-surface inhomogeneity of stress and chemical potential distributions is characterized by two parameters. One parameter is associated with the local mass displacement and the other is due to the dissipative processes in the body.