Axisymmetrical swirling boundary layers and fully three-dimensional layers have in common a two-component shear stress. Since the former are amenable to treatment by two-dimension al computational methods, they constitute useful and economical testing terrain for advanced turbulence models. Traditional based turbulence models, arbitrarily extended to account for the influence of a swirl component of velocity, display a serious lack of universality. A high Reynolds number turbulence model is developed in the present study which provides algebraic equations for all six Reynolds stresses. The model and its mixing-length derivative are both employed to predict a variety of swirling boundary layers. A promising improvement in universality of predictive power is exhibited. The principal conclusion is that future research should concentrate on extending the applicability of stress turbulence models into the sublayer region since the effective-viscosity based models are least satisfactory there.