The spontaneous coronary artery dissection (SCAD) is a clinical complication of angioplasty leading to an initiation of a tear/crack in the intima layer of the artery. The crack can propagate to the interface of the intima-media layer following by intramural hematoma. The relation between the SCAD and atherosclerosis is a controversial issue, as some studies stated no correlation between them while others showed that a crack can initiate in the intima but cannot propagate into the atrophied media layer. To investigate the relation between the intraluminal crack propagation in the atherosclerotic artery and SCAD, this study numerically investigated the initiation and propagation of a crack in the intraluminal and radial locations of the healthy and atherosclerotic human coronary arterial walls. The energy release rate, namely J-integral, is computed as a numerical derivative of the strain energy with respect to a crack extension using a user-defined virtual crack method (VCE) of extended finite element method (XFEM). Experimental measurements were carried out to calculate the elasto-plastic mechanical properties of the healthy and atherosclerotic human coronary arteries. The experimental data were then assigned to our own established patient-specific FE model of the coronary artery. Cracks were sketched in the intraluminal and radial locations of the arterial wall and allowed to propagate to the virtual interface of the intima-media to form a false lumen. The results revealed a higher stress at the crack tip of the healthy arterial wall compared to the atherosclerotic one. Lower crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) were observed in the intraluminal crack of the atherosclerotic artery. J-integral of the atherosclerotic arterial wall was also found to be higher than the healthy one at the intraluminal crack. The results revealed that although a crack can initiate in the intraluminal of an atherosclerotic artery, it cannot propagate into the media layer due to a relatively higher rate of the strain energy release in the atherosclerotic arterial wall compared to the healthy one.