A precise knowledge of the distribution of internal stresses in materials is key to the prediction of magnetic and mechanical performance and lifetime of many industrial devices. This is the reason why many efforts have been made to develop and enhance the techniques for the non-destructive evaluation of stress. In the case of magnetic materials, the use of eddy current (EC) techniques is a promising pathway to stress evaluation. The principle is based on the significant changes in magnetic permeability of magnetic materials subjected to mechanical stress. These modifications of magnetic permeability affect in turn the signal obtained from an EC probe inspecting the material. From this principle, a numerical tool is proposed in this paper to predict the EC signal obtained from a material subjected to stress. This numerical tool is a combination of a 3D finite element approach with a magneto-mechanical constitutive law describing the effect of stress on the magnetic permeability. The model provides the variations of impedance of an EC probe as a function of stress. An experimental setup in which a magnetic material subjected to a tension stress is inspected using EC techniques is tailored in order to validate the model. A very good agreement is found between experimental and modelling results. For the Iron-Cobalt alloy tested in this study, it is shown that a uniaxial tensile stress can be detected with an error lower than 3 MPa in the range from 0 to 100 MPa.