Abstract: Taking the second-order-moment and power of the bucket as the beam width definition, changes of the beam parameters such as the beam width and farfield divergence angle of Gaussian beams after passing through an astigmatic lens are studied both analytically and numerically. It is found that the relative errors of the beam width and far-field divergence angle introduced by the astigmatism depend on the astigmatic coefficient, the Rayleigh range and the focal length of the lens. For the beam width, the errors also depend on the propagation distance. At the geometrical focal plane the relative errors in the x and y directions are equal. The results are of practical interest for the design of laser optics systems.