Finite element technique is used to model the free surface flow regime representing injection mould filling of elastomeric material such as rubber compounds. The most distinct feature of the constitutive behaviour of elastomers, is the influence of material elasticity on the elongation and shear deformation suffered by the fluid during flow. In the present study this feature has been tackled through the use of Criminale-Erickson-Fibley (CEF) model. A scheme based on the Volume of Fluid technique is developed for free surface tracking. The results represented in this paper have also been compared against the Phan-Thien/Tanner model and are shown to be in closer agreement with the theoretical expectations than those obtained by the P-TIT equation. The results prove the applicability of the developed model to industrially relevant situations.