A series of large eddy simulations of plane Couette flow has been performed for Reynolds numbers between 750 and 3750. Three different models were used for the sub-grid scale stresses, and the results were found to be in reasonable agreement with existing data. The results were used to calculate Cμ, the coefficient in the standard k−ε turbulence model. It was found that in the near-wall region, significantly lower values of this coefficient were predicted, compared to correlations based on channel flow. One possible explanation could be that the boundary has a greater influence on the turbulence in the case of Couette flow in which there is no mean pressure gradient.