This paper is to report enhancement of engineering J estimation for semi-elliptical surface cracks under tensile load. Firstly, limitation of the sole solution suggested by Zahoor is shown for reliable structural integrity assessment of thin-walled nuclear pipes. An improved solution is then developed based on extensive 3D FE analyses employing deformation plasticity theory for typical nuclear piping materials. It takes over the structure of the existing solution but provides new tabulated plastic influence functions to cover a wide range of pipe geometry and crack shape. Furthermore, to facilitate easy prediction of the plastic influence function, an alternative simple equation is also developed by using a statistical response surface method. The proposed $H_1$ values can be used for elastic-plastic fracture analyses of thin-walled pipes with a circumferential surface crack subjected to tensile loading.