Previous studies on Z-scan have paid little attention to Z-scan transmittance about elliptical Gaussian beams in thick Kerr media. The purpose of this study is twofold. First, it proposes a new analytical approach to the Z-scan on-axis transmittance for elliptical Gaussian beams through the variational method. The analytical approach yields an explicit analytical solution (not numerically analyzed solution) for the Z-scan on-axis transmittance in arbitrary thick media, and then the explicit solution is generalized to circularly or elliptically symmetric Gaussian beams. With the analytical solutions, we explain the mechanism of the elliptical beam waist changes in both positive and negative Kerr media. Second, the proposed solutions are experimentally tested in the photorefractive LiNbO3:Fe crystal with a cw Ti:sapphire elliptical laser beam (lambda = 800 nm), showing congruence between experimental data and the predicted values from the solutions. (C) 2016 Elsevier B.V. All rights reserved.