Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well known Kirchoff-Fresnel diffraction equation. In this paper Gaussian and super-Gaussian beam shapes are propagated both through free space, and through a nonlinearly absorbing medium. The results show that shape invariance during propagation is dependent on the medium under consideration, and we find that super-Gaussian fields are shape invariant in certain nonlinearly absorbing media.