We report an investigation of the popular Z-scan technique for elliptical Gaussian beams. A thin lens wave optics theory is developed for such a beam by generalizing the existing theory for circular Gaussian beams. We find that the Z-scan signature is greatly influenced by two parameters, namely, the ellipticity of the input beam and the waist separation. Depending on these parameters, an additional peak and valley may appear in a closed-aperture Z scan, whereas a small asymmetry may be observed in an open-aperture Z scan. We demonstrate what the qualitative features of both open and closed Z scans would be for a beam with any ellipticity. (C) 1996 Optical Society of America