The low Reynolds number stress-omega model is applied to flow associated with a rotating cylinder operating in a larger, stationary cylinder. The working fluid fills the gap between the cylinders. Direct numerical simulation data are used to test the predictions by this turbulence model. Previous work has shown that simpler models are unable to predict with reasonable accuracy the wall shear stress experienced by the rotating cylinder. The present study with a more complex turbulence model shows that the wall shear stress on the rotating cylinder is underestimated significantly. Examination of turbulence velocity fluctuation intensity distributions points to underprediction of the streamwise turbulence level and excessive values of the wall normal turbulence level. Results are given for no shear and a wall shear at the outer cylinder surface but no effect on the inner cylinder statistics was found. An examination of the Reynolds stress anisotropy tensor components highlights a significant deficiency in this parameter which is an essential component of the pressure-strain modelling of Reynolds stress models. The most significant aspect is a rapid decrease of the streamwise component of the Reynolds stress anisotropy tensor relative to the direct numerical simulation results and values which are too low for the other two components.