The present work presents a 3D thermo-mechanical model and its application to the casting of square multi-crystalline silicon ingots. Stresses and deformations in the ingot are the results of the combined effects of thermal contractions and mechanical loads induced by the ingot-crucible interaction. The model accounts for plastic deformation at high temperature. Air gap formation, sticking and fracture of the coating layer are all considered while modelling the ingot-crucible contact. The model is applied to analyse the crystallisation and cooling process in a vertical Bridgman furnace. Several situations are studied to illustrate ingot-crucible interactions (air gap formation, partial sticking and loss of contact due to fracture of the coating layer) and their consequences on the residual stress and strain fields. The 3D evolution of air gap formation between the ingot and the crucible is also presented.