Adding simply, in the classical capillary model, a constant line density of energy along the contact line leads to ill-posed equilibrium problems. Then, when line tension is present, the equilibrium configuration minimizes a different energy: the relaxedenergy, which explicitly depends on the presence of surface phases (i. e. infinitesimal films) on the boundary of the container. This formulation enables us to describe the modifications of the Young's law and then of equilibrium configurations which are due to line tension.