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The aim of the paper is the determination of the propagation path of an in-plane perturbed tunnel-crack embedded in an infinite isotropic elastic body loaded in puremode I through some uniform stress applied at infinity. The crack advance is supposedto be governed by the stress intensity factor, through Paris’ law in fatigue and Irwin’scriterion in brittle fracture. In practice, the advance is computed in both fatigue andbrittle fracture by a Paris’ type law, Irwin’s criterion being regularized by a procedureanalogous to the “viscoplastic regularization” in plasticity. The necessary determinationof the stress intensity factor along the front for all the stages of propagation is achieved bysuccessive iterations of Bueckner-Rice weight-function theory, that gives the variation ofthe stress intensity factor along the crack front arising from some small arbitrary coplanarperturbation of the front. It is closely linked to previous numerical works of Bower andOrtiz [1] and revisited by Lazarus [2] for closed crack fronts. It is adapted here to thetunnel-crack, that is to two crack fronts. In fatigue, two kinds of propagation paths canbe distinguished depending on the width of the perturbation. If this width is less thana critical value, the perturbation vanishes, so that the front becomes rectilinear (stablecase). Otherwise, the perturbation increases so that the front becomes more and moreperturbed (unstable case). The numerical study allows us, however to study the non-linear effects due to the finite size of the perturbation. It is noticed that these effectsenhance the instability and slacken the come-back to the rectilinear configuration in thestable case. In brittle fracture, it appears that the perturbation increases in width andthen in amplitude; that is, it behaves in a kind of unstable manner whatever the initialperturbation.