We propose a method for incorporating, in a simple and effective way, surface tension phenomena in fluid or solid mechanics numerical simulations. The only requirements are 1) to use the finite element method (FEM), rather than other classical approaches; 2) to develop surface elements having a special, albeit very simple, constitutive law. The principle consists of, instead of accounting for surface tension through the loads it induces upon the underlying medium, incorporating it through its physical mechanism, that is, creation of a tight membrane on the surface of the medium. This implies, within the FEM, meshing the surface with 2D elements in which the (2D) stress state is purely hydrostatic, with diagonal components equal to the surface tension (instead of being as usual a function of the velocity or displacement gradient). The principle of virtual work serving as a basis of the FEM ensures equilibrium of the tight membrane, and transmission of efforts on the underlying medium is warranted by coincidence of the nodes of the membrane and this medium.