Objective The circumferential and axial propagation of crack in the media layer of aorta is called in-plane propagation, which is essentially the delamination and separation of adjacent elastic lamellae within the media. The interface damage of the aortic wall occurs during the delamination, which resulted in aortic dissection. The crack is also known as false lumen (FL) of the dissection in clinic. Based on interface damage, a numerical simulation method for in-plane propagation of FL is proposed to explore the law of in-plane propagation of the initial cavity. Methods Three interface damage modes are characterized by bilinear traction separation law, and the damage parameters are calibrated by simulating peeling and shearing tests. The damage interface is introduced into the ideal double-layer cylindrical tube aortic model by means of cohesive zone model to simulate the in-plane propagation of FL. The control variable method is used to change the circumferential angle, axial length and radial depth of the initial cavity, and several calculation models are established to investigate the influence of cavity geometry parameters on the propagation direction, critical pressure and interface damage mode. Results It is shown that the interface damage is mainly opening mode (mode I) in axial propagation and sliding mode (Mode II) in circumferential propagation. With the increase of the radial depth of the initial cavity, the propagation direction of the FL changes from circumferential to axial, the critical pressure decreases (i.e. it is easier to propagate), and the axial damage tends to be pure opening mode. With the increase of the circumferential angle and axial length of the initial cavity, the critical pressure decreases and the circumferential damage tends to be pure sliding mode. The critical pressure of single damage is lower than that of mixed damage. Conclusion This study shows that the cohesive zone model can effectively characterize the interface damage behavior of elastic lamellae within the media, therefore, it is suitable for the numerical simulation of in-plane propagation of the FL. The numerical simulation results show that the geometry characteristics of the false lumen have an important effect on the in-plane propagation of the dissection. This paper is helpful to understand the complex pathophysiological process of dissection crack propagation.