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The conventional method for predicting the shape change of a surface crack in a round bar simply utilizes the Paris-Erdogan law with the least squares method using a certain shape assumption with excessive constraints. In this paper, a three-parameter model for a round bar subjected to tension is developed with fewer shape assumption restraints by employing a fatigue crack growth circles method. The equivalent stress intensity factor <inline-formula> <math display="inline"> <semantics> <mrow> <mo>&#916;</mo> <msub> <mi>K</mi> <mi>e</mi> </msub> </mrow> </semantics> </math> </inline-formula> based on both stress intensity factors along the current and new crack front is used to reduce the total number of increments. The results show that the proposed method has a good convergence speed and accurate prediction of crack shapes. The present method is validated by comparing the solution with other simulation solutions and experimental data.