One of the most frequently encountered problems in joint structures is interfacial cracking, sometimes also known as delamination. The stress intensity factors of a crack between dissimilar media are important parameters for evaluating delamination strength. A new method is proposed for the stress intensity factor analysis of a crack between dissimilar anisotropic materials under mechanical and thermal stresses. In the present method, the M-integral method that is an extended J-integral in conjunction with the finite element method was used to calculate individual stress intensity factors, K_I, K_<II> and K_<III>. The present method was applied to some interface crack problems under mechanical and thermal loads. The results are compared with analytical solutions. It is shown that the energy release rate and stress intensity factors obtained by the present method are very accurate.