Vortex beam is one of the current research hotspots, with the deepening of research, its transmission characteristics in the medium has also been paid attention to. Based on the nonlinear wave equation, the split-step Fourier algorithm is used to numerically simulate the amplification characteristics of square vortex beams in Nd:YAG media. The effects of topological charge, incident peak light intensity, beam waist width and beam order on the intensity, spectrum and B-integral of a square vortex beam are studied. The numerical results show that when the square vortex beam is amplified by Nd:YAG medium, the intensity fluctuation of the center position is stronger, but the intensity fluctuation of the edge of the beam is weaker. The intensity of the central region of the outgoing beam oscillates continuously, and the intensity in the diagonal direction is stronger than that in the axial direction. Small topological charge and large waist width of the square vortex beam can slow down the central intensity oscillation of the beam through Nd:YAG medium, and reduce the influence of Kerr effect on beam amplification. In addition, reducing the thickness of the Nd:YAG medium can reduce the intensity of the beam center and reduce the size of the B-integral.