Since 2004, the wooden support of Mona Lisa has been studied by an international research team formed by specialists of wood science and optical measurements, interacting closely with curators and restorers, to evaluate the climatic specifications adopted for the then new climate-controlled display case, assess the risk of propagation of a historical crack affecting the Panel, suggest possible improvements to the Panel’s framing, and improve the technological aspects of the current monitoring procedure. The study has been carried out mainly by direct observation and measurements during the yearly opening of the display case, by continuous monitoring of the Panel’s mechanical behaviour and by developing a predictive numerical model based on the finite element method. This paper deals with the following topics: (i) a technological description of the Panel and of its framing, (ii) the non-invasive measurement equipment and monitoring methods developed, (iii) the simulations of the hygro-mechanical behaviour, (iv) the most significant results obtained so far, including the derivation of the elastic parameters of the wooden Panel, the description of the contact zones between Panel and framing, the evaluation of contact forces and possible actions for improving the framing. The model implementation evidences the correspondence between principal strains in the Panel and craquelure patterns in the paint layers, and allows assessing the crack propagation risk.