Functionally graded materials (FGMs) are multi-phase inhomogeneous composites, possessing smooth spatial variations in certain physical properties of the constituents. Depending on the types of the constituent materials used in the processing of orthotropic FGMs, the influences of thermal and hygroscopic loadings could be rather significant. This study is directed towards developing a new computational fracture analysis technique for orthotropic FGMs that are under mixed-mode hygrothermal loading. The method is based on the use of the J-integral in conjunction with the asymptotic crack tip displacement fields. Developed computational technique is integrated into a finite element analysis software. Parametric analyses are carried out by considering an inclined edge crack in an orthotropic FGM layer that is subjected to the influence of hygrothermal loading. In order to be able to verify the proposed method, obtained results are compared to those computed via displacement correlation technique (DCT). Comparisons demonstrate that proposed technique leads to numerical results of high accuracy. Further results are provided to illustrate the influences of crack inclination angle and geometry on the temperature and the specific moisture concentration fields; and the modes I and II stress intensity factors.