Abstract: The lack of penetration (LOP) is a very common type of discontinuities in welds,so that how to simplify it more scientifically and reasonable and therefore to conduct its fracture analysis are a problem continuously interested to engineering and academic circles.In this paper,several common root shapes were chosen among the photos of LOP's root profiles and five typical sorts of notches with regular root shapes were obtained after some extent simplification to the LOP's root shapes.Based on this,the elastic plastic finite element method was adopted in the paper.The finite element calculations were conducted by taking the geometrical shapes and sizes of nothch root as parameters and a series of J-L_r curves were gotten.Through analyzing the curves,the main factors influencing the value of J-integral can be found,they were the notch wedth or the notch root curvature and the shapes of notch,and finally the root shape with the maximum J-integral value was derived to be the flat end shape.Therefor,the values of LOP's J-integral can be calculated simply and conservatively by adopting the notch with a flat end proposed in this paper,and furthermore the engineering calculations of LOP's J-integral values can be realized.