Although the standard k-epsilon model is most frequently used for turbulence modeling, it often leads to poor results for strongly swirling flows involved in stirred tanks and other processing devices. In this work, a swirling number, R-s, is introduced to modify the standard k-epsilon model. A Eulerian-Eulerian model is employed to describe the gas-liquid, two-phase flow in a baffled stirred tank with a Rushton impeller. The momentum and the continuity equations are discretized using the finite difference method and solved by the SIMPLE algorithm. The inner-outer iterative algorithm is used to account for the interaction between the rotating impeller and the static baffles. The predictions, both with and without R-s corrections, are compared with the literature data, which illustrates that the swirling modification could improve the numerical simulation of gas-liquid turbulent flow in stirred tanks.