Cylindrical shells are an important structural element in engineering and construction. Problems in the design and operation of various pipelines, supports of offshore constructions, modeled by inhomogeneous cylindrical shells are relevant for modern industry. The inhomogeneity of elastic properties can be incorporated both initially and arise as a result of operation. The paper analyses a shell whose inhomogeneous elastic parameters depend on the radial coordinate and these dependences can be described by a piecewise continuous functions. Free harmonic vibrations of Kirchhoff-Love type shell are considered. The area of applicability of various models of averaging of inhomogeneous shell parameters is analyzed on the example of a two-layer shell with material density inhomogeneity. On the basis of the exact analytical solution, the influence of inhomogeneity on the shell natural frequencies for shell modes is investigated. The comparison with previously obtained results on finite element package ANSYS (taken as a reference) is fulfilled.