We consider the following problem: how determine non-uniformly distributed static residual stresses on the bases of values of elastic processes of small amplitude measured at the boundary of a layered semi-restricted body. Using the method of small parameter, we propose a procedure which ensure the solution of the problem; this procedure employs the assumption of weak dependencies of the values of elastic modulus on the values of residual stresses and the assumption of small incurvature of all the boundaries (both external and internal) of layers. As an example, we consider the case where the distribution of residual stresses depends on only one spatial variable, the distance measured from the external surface of the body.