Abstract: Self-focusing rings of circle symmetric super-Gaussian laser beam (CSSGLB) with high intensity travelling in Nd:glass medium, are described in detail with numerically solution to the nonlinear Schdinger equation. When a CSSGLB with initial perturbations travelling in this medium, the self-focusing rings are to be broken up and form high intense filaments. This phenomenon showed the instability of the self-focusing rings .The high intensity filaments may destroy the medium．