Abstract: Finite element method was used to analyze the J integral evaluation method for a cylindrical specimen with deep circumferential crack under axial or torsional load.First,the relationship between axial or torsional load and axial or angular displacement of cylindrical specimens with different circumferential crack depth was determined.Then,two methods were used to calculate the J integral.One is the simple method that calculates the J integral by a single specimen's load-displacement relationship;the other is the energy method.The J integral obtained by the simple method agrees well with that determined by the energy method using multiple medium carbon steel specimens with a circumferential crack,as far as the crack depth is deep enough or the axial or angular displacement is small.