The objective of this study is to present numerical aspects related to the implementation of the interaction integral method for the purpose of determining the stress intensity factors in mode I and mixed-mode crack problems of functionally graded materials (FGM) and homogenous materials for a different form of cracking. This numerical development is based on the use of the finite element method (FEM), by the coupling of the Ansys-Matlab calculation codes. To validate the accuracy and reliability of the approach, the results obtained will be compared with other numerical results in the literature. The interaction integral method is one of the methods most compatible with the formulation of the finite element method. Therefore, we are interested in this study, in terms of the presentation of necessary steps which allow the resolution of a problem by finite elements for the mechanical problems. It is very important to note that the principle of the implementation of the “Integral M” technique is using scripts based on the coupling of two commercial software.