This paper presents a study of the self-focusing and self-defocusing of elliptically shaped Gaussian laser beams in collisional and collisionless plasmas. The non-linear dependence of the dielectric constant inside a collisional plasma is due to inhomogeneous heating of energy carriers and in a collisionless plasma it is due to the ponderomotive force. It is found that the beam gets focused at different points in different planes, exhibiting the effect of astigmatism. In certain power regions considered, the beam either converges or defocuses in both the directions, while in some other regions of the power spectrum one dimension of the beam focuses while the other defocuses. The beam also propagates in an oscillatory waveguide.