This work was originated with an industrial problem, the process of coating of rods with a enamel. The task was described mathematically the process such as it can be controlled, in order to avoid losses and to optimating the production. In this work the problem is formulated and solved. Furthermore, a theory of interfaces is formulated, like that exist in free or moving boundary flows, when the surface tension is a dominating force. The formulation of the theory is made within the continuous media mechanics point of view, and the interface is modeled as a bidimensional body separating and interacting with tridimensional bodies. Of course, the interface is a part of the bodies. The theory is developed and applied to several free boundary problems in order to show its adaptability. One of the principal goals of this work is the development of an algorithm and the computational program for computing equilibrium capillary surfaces.