To improve the efficiency of turbine and jet-engine combustors, a swirling flow is often used to enhance the flame stability and increase the fuel-air mixing. The accurate prediction of turbulent swirling flows will improve the design of combustion system. Since swirl has strong influence on the turbulence characteristics, many studies have been carried out to aid our understanding of the complex physical phenomena and to establish more reliable models for the flow predictions. The widely-used k-e turbulence model fails to predict the swirl flows accurately. The second-order Reynolds stress turbulence model (RSTM), offering the anisotropic eddy viscosity concept, provides more physical insights for the modeling of swirling flows. While RSTM involves the solution of a number of stiff transport equations for stresses, the explicit algebraic Reynolds stress model (EARSM) can be considered a cheaper alternative of RSTM. EARSM results in nonlinear k-e model, which not only allows a straightforward extension of the original k-e model, but also retains the anisotropic eddy viscosity concept of RSTM. In the present paper, we shall compare EARSM with the standard k-e model in predicting a number of swirl flows. Comparison with experiments will be provided.