The work presented here is concerned with the free vibration analysis of cylindrical storage tanks with axial thickness variation and partially filled with fluid. The tank is modelled using FlΓΌgge's thin shell theory and the fluid in the tank is assumed to be inviscid and imcompressible, governed by the potential flow theory. The coupled partial differential equations for this fluid-structure interaction problem, subject to appropriate boundary and continuity conditions, are solved analytically for the case of a constant thickness tank. Using this solution as the basis for analyzing a variable thickness tank which is discretized into a series of constant thickness elements, a general procedure via the transfer matrix technique is suggested. The adoption of this approach implies that tanks with any type of axial non-uniformity with respect to both thickness and cross-sectional area can be handled. Parametric studies involving a variable thickness tank the wall thickness of which is linearly varying and an equivalent constant thickness tank are performed. The resulting eigensolutions of natural frequencies and their associated free vibration mode shapes demonstrate the versatility and accuracy of the proposed technique.