We present a new methodology to simulate viscoelastic flows with free-surfaces. These simulations are motivated by the modelling of polymers manufacturing techniques, such as extrusion and injection moulding. One of the consequences of viscoelasticity is that polymeric materials have a “memory” of their past deformations. This generates some numerical difficulties which are addressed with the log-conformation transformation. The main novelty of this work lies on the use of the volume-of-fluid method to track the free surfaces of the viscoelastic flows. We present some preliminary results of test case simulations where the different features of the model are tested independently.