Many materials exhibit a yield stress below which they do not flow. The present report explores their rheology and discusses the numerical modeling of doughlike materials with yield stress using a general purpose computer code based on the Galerkin form of the finite‐element method. Some results are given validating the general purpose algorithm, and the effects of yield stress on extrudate swell is discussed. In conclusion a comparison is made between numerical predictions and experimental observations for exit temperature and extrudate swell profiles of a viscoelastic material with yield stress as extruded through an axisymmetric die. The presence of a yield stress is found to reduce swelling dramatically.