To calculate the rate of crack growth, one approach is to make use of the parameter Stress intensity factors (SIF). Although many researches have been contributed to find the reliable solution of stress intensity factors, there is the restriction on the validity range for the crack depth and crack length. Another point should be considered is that FGM (functional graded material) is more popular at present. This research is about to find the stress intensity factor of the crack in FGM plate members under axial tension loading, of the cracked FGM plate members. With these proposed SIF, by using Finite Element Method and based on the principle of Elastic-Plastic Fracture Mechanics, the v influences of crack configuration in FGM plate can be explored. It will not only make a contribution on establishing time interval of maintenance plate in use but also help to forecast the time limit for repair. In this report, the stress intensity factors for circumferential semi-elliptical surface cracks under axial tension loading in FGM plate members which provide a difference material (The difference presented by the value of Young’s modules and passion ratio.) in thickness direction are presented. The work has produced a trend of stress intensity factors with the variation of parameter a/T, c/a for surface cracks