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In this paper, the stress intensity factor K  for the crack front line α − ε (1 + cosmθ ) , which is slightly perturbed from a complete circular line with a radius of α, is solved. The mathematical procedure chosen in this study is based upon the perturbation technique developed by Rice for solving the elastic problem of a crack whose front slightly deviates from some reference geometry. It is shown that the solution obtained for the stress intensity factor matches the results of a three-dimensional finite element analysis.