Abstract: In order to study propagation properties of Hermite-Gaussian beams in photorefractive saturable nonlinear media, finite difference method was used to solve the evolution equation of light wave numerically and analyze the propagation properties of Hermite-Gaussian beams theoretically. The results show that, under suitable nonlinear conditions, 1-D Hermite-Gaussian beams of 1-order, 2-order and 3-order can form the solitons in respiratory mode during the propagation in photorefractive nonlinear media. With the increase of nonlinearity, the separation tendency among light field components of Hermite-Gaussian beams would become weaker. At the same time, the amplitude fluctuation effect of each light field component would be more obvious. The changes of incident position and incident angle of Hermite-Gaussian beams have no influence on its propagation characteristics. The transmission characteristics of 2-D Hermite-Gaussian beams are similar to those of 1-D. These properties of Hermite-Gaussian beams have certain application prospects in the field of optical switching.