This paper is concerned with the development of a numerical method for the computation of two-dimensional time-dependent free-surface problems where surface tension cannot be neglected. The imposition of a surface tension force in a finite element method requires the evaluation of a line integral where the curvature R of the interface has to be accurately evaluated. In this paper, we demonstrate how this line integral can be replaced by a volume integral over the entire domain avoiding the explicit computation of R. The proposed method is then applied to the computation of the complex deformation of a drop of a viscous fluid immersed in another fluid and submitted to a shearing flow field.