A numerical implementation of the Volume of Fluid (VOF) free surface technique, applied to a filling process governed by a potential flow, is introduced. The implementation is based on a finite element control volume space discretization and uses an implicit time integration. This allows for the accurate tracking of the filling front using large simulation time steps in molds with complex geometries. The approach is validated on comparision with the analytical solution for filling a one‐dimensional tube and with two‐dimensional results obtained with previously‐presented filling algorithms. Examples of the application of the approach in the analysis of structural resin transfer molding (SRTM) are presented. The capability of the method is demonstrated on predicting “race tracking” and “dry spotting” phenomena. The CPU requirement for a typical analysis is on the order of 1 to 20 s on pesonal computers.