A numerical FEM (Finite Element Method) model was implemented to represent the mechanical state of the wooden panel of the Mona Lisa, as it is conserved in its exhibition case, and constrained in its auxiliary frame. The model is based on the integration of advanced numerical analysis and various experimental examinations carried out non-invasively on the artwork by the authors during over 15 years. This includes visual, microscopic and X-ray observations together with mechanical measurements and monitoring of panel deformations and constraining external forces. In addition to the development of non-invasive techniques to characterise the mechanical properties of the panel, the FEM model reliably evaluated the strains and stresses generated in the panel by the various actions it experiences. The paper consists of the following parts: (i) a short summary of the experimental measurements and other observations, (ii) a detailed description of the FEM numerical model, of the hypotheses it is based on, and of its advantages and limits, (iii) the main results obtained by running the model. This includes the identification of local strains and stresses, the location of most critical areas, an evaluation of the risk that the existing ancient crack may propagate, and an evaluation of safe ranges for the forces acting on the wooden panel, (iv) the validation criteria for such results, and (v) a discussion about the significance of the mechanical model.