A theory of self-mode-locking of Ti:sapphire laser is described. A nonlinearABCD matrix,derived from the aberrationless theory of self-focusing, is introduced to treatthe propagation of Gaussian beams in materials with Kerr nonlinearity,showing that selffocusing in the laser rod leads to modification of the Gaussian beam parameters either in therod or on the resonator mirrors.An optimum resonator design for Kerr-lens-mode-lockingwith(or without) hard-aperture is given.A theoretical prediction is confirmed by the experimental result.