This study is concerned with the flow behaviour of a rubber compound in capillary and injection moulding dies in the temperature range of 80–120°C. The injection moulding die designs had a tapered angle ranging from 40° up to 150°. The rheological characterisation of the rubber compound in the capillary dies showed that rubber slips at the wall, and this was modelled with an appropriate slip law. The pressure drops in the system were measured for all tapered dies. Numerical simulations were then carried out with a purely viscous (Carreau) model and a multimode viscoelastic (K-BKZ) model. The results showed a good agreement with the experiments for both the capillary and the injection moulding dies, provided that slip is included in the simulations as determined experimentally.