Problems in the design and operation of various pipelines modelled by inhomogeneous cylindrical shells remain relevant for modern economics. Inhomogeneity of elastic properties can be incorporated both in the design and arise as a result of operation. In this paper, the inhomogeneous shell is modelled by a thin elastic shell whose inhomogeneous properties depend only on the radial variable. Free vibrations of Kirchhoff-Love type shell are considered. On the basis of an exact analytical solution, the influence of inhomogeneity on the natural frequencies of axisymmetric modes is investigated on the example of a bilayer shell with inhomogeneous material density. The multidirectional change of frequency with the growth of the reduced density of the inner layer is analysed for the case of modes with numbers less than two and for modes with numbers greater than one. The mechanisms of such frequency behaviour and the applicability of different models of averaging of inhomogeneous shell parameters for each of these cases are analysed. The comparison with previously obtained results on finite element package ANSYS (taken as a reference) is fulfilled.