We compute and study critical pressures (Pc) for the initiation of the propagation of an existing arterial dissection, which in general depends on the residual stress and pre-stretch of the artery, and the length and depth of the tear, using the Holzapfel-Gasser-Ogden mathematical model for the walls of the large arteries. For the simple case of a 2D tissue sample, increasing the length of the initial dissection lowers the value of Pc, but when the strip is supported by connective tissue, arrest of the dissection is obtained. A peeling test on a disc-shaped sample demonstrates that the orientation of collagen fibres plays an important role in the direction of propagation. To study the effects of residual stress on arterial dissection, we include residual stress, quantified by the opening angle when an artery is subject to a longitudinal cut. We show that Pc is approximately proportional to the opening angle, so that the observed loss of residual stress associated with ageing increases the likelihood of dissection. Finally the effects of the circumferential (arc) length and radial position of the initial tear in a cylindrical model of an artery are investigated. Pc decreases as arc length increases and as the initial dissection is placed closer to the lumen. Prolapse of the dissection into the lumen occurs when the initial tear close to the lumen and the arc length is large.