Herein, for the propagation and interaction of finite energy Airy-Hermite-Gaussian (FEAHG) beams in a medium with a potential well, a linear parabolic (Schr dinger-like) equation was applied as the theoretical model in a split-step Fourier numerical simulation. Results show that the optical field structure of FEAHG beams rotates in the medium with a potential well. The greater the intensity of the potential well is, the shorter the propagation distance for the optical field structure completing rotation is. In addition, further investigation of the interaction between two FEAHG beams with different initial intervals in the medium with a potential well reveals that the number of light spots during propagation changes.