The analysis of existing methods for modeling the elastic characteristics of materials is carried out. It is taken into account the one-dimensional continuous inhomogeneity of the elastic characteristics. In contrast to the known monotone functional dependencies that describe the distribution of mechanical characteristics of elastic bodies along one direction, we propose models for describing inhomogeneous elastic properties of materials that are non-monotonically distributed along one coordinate. An approximate analytical solution of the Lame problem is obtained for a specific non-monotonic distribution of the displacement modulus along the radial coordinate. The solution is obtained in the form of a convergent sequence of approximations. A numerical experiment is performed for specific values of the approximating coefficients and the results are analyzed.