We report on theoretical study of optical singularity birth in a wave front of light beam with astigmatic Gaussian profile passing through a homeotropically aligned nematic liquid crystal (NLC) cell. When a lineary polarised astigmatic Gaussian light beam illuminates the cell, the light induced Frederick's transition can be observed. Ritz's variational method is used, i.e. the profile of director reorientation is considered to be similar to astigmatic Gaussian profile. Parameters of the trial function are calculated numerically. The threshold intensity of light beam is appeared to increase with increasing of asymmetry of the beam under the constant value of laser beam area and cell thickness. Utilizing the Huygens-Fresnel principle and geometrical optics approximation we calculate the amplitude distribution in space for different distances from the cell. It is obtained that the trajectory of zero amplitude resembles a deformed rubber ring symmetrical in the xz-, yz-planes and stretched along z-axis.