A fluid dynamic analysis package, PolyFlow, based on the finite element method is used to study the sharkskin phenomenon. A stick-slip mechanism is used as the basis for the simulations. This study is aimed at illustrating how fluctuations in the stress at the exit from the die cause similar fluctuations in the extrudate swell ratio, resembling the sharkskin phenomenon. Such fluctuations in the stress at the exit from the die are produced by implementing a stick-slip boundary condition at the die wall, mimicking a mechanism of molecular entanglement/disentanglement at the wall. We use a superposition of stress relaxation/stress growth and a periodic change in extrudate swell governed by the die exit stress level to depict sharkskin. Three relatively monodisperse polybutadienes were used in this study. The simulated sharkskin time period was found to be in good agreement with experimental findings. We found that the simulated pictures of sharkskin are similar for all three molecular weight samples. A comparison between the simulated sharkskin and experimental results show qualitative resemblance. The main problems preventing us from generating more quantitative sharkskin results mainly reside in the model limitations in depicting stress singularity, limitations in mesh design refinement and the constitutive model employed. In spite of these limitations, the qualitative agreement between simulation results and experimental data is good.