We propose a scheme of efficient solving an inverse coefficient problem on a reconstruction of unknown laws of variation of mechanical properties of inhomogeneous isotropic cylindrical region. The reconstruction is performed step‐by‐step by means of solving two problems on torsional and radial vibrations of the considered region that provides a formulation of two inverse problems on searching the unknown functions. We build iterative processes of solving the inverse problems stated; in frames of each process, we derive systems of the Fredholm integral equations of the 1st and the 2nd kind in order to find corrections to the unknown functions relative to the corresponding initial approximations. We conduct the computational experiments on a reconstruction of the unknown dimensionless functions.

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