A computational fluid dynamics algorithm that uses a volume of fluid method to model immiscible phase behaviour is adapted to simulate the flow of viscoelastic fluids. Two-dimensional Cartesian simulations of a viscoelastic droplet passing through a contraction are compared against experimental results generated using a three-dimensional planar contraction. Viscoelastic effects are simulated using the Oldroyd-B rheological model. The physical and numerical models capture the deformation process well, particularly the characteristic forked tail that develops on the viscoelastic droplet while it is within the contraction. Encapsulation of continuous phase fluid is observed in the experiments, but not predicted by the simulations. We suggest this is due to inadequate mesh refinement at the length scale of a fine thread entrainment process. The numerical results show the existence of an elastic stress within the droplet that could cause the entrainment and subsequent encapsulation. The process has application potential in the manufacture of micron-sized drug and chemical delivery capsules. (C) 2008 Elsevier B.V. All rights reserved.