The effect of roughness is a change in the velocity and turbulence distributions near the surface. Turbulence models with surface roughness effect are applied to the fully developed flow in a two-dimensional, rough wall channel. Modified wall function model, low-Reynolds number k-$varepsilon$ model, and k-$omega$ model are selected for comparison. In order to make a fair comparison, the calculation results are compared with the experimental data. The modified wall function model and the low-Reynolds number k-$varepsilon$ model require further refinement, while the k-$omega$ model of Wilcox performs remarkably well over a wide range of roughness values.