The effect of elliptic Gauss beam on the focusing of the signal beam under the other different parameters is discussed. There are six parameters, i.e. the wavelength ratio of the pump beam to the signal, the initial amplitudes of a pump beam and a signal beam, the initial separation between the beams' centers, and the ratio of the initial beam width of the X and Y of the pump to that of the signal, which influence the induced focusing of the signal optical beam. The numerical simulations are in good agreement with the experimental results obtained by Hickmann in 1992.