A numerical analysis for a flow induced by the Rushton disc turbine was done by a finite element method. As flows in the vessel depend on the geometry of the impellers and the vessels, unstructured mesh was used in order to consider their geometries accurately. Moreover, elements used were a hybrid composed of tetrahedral and prism, which could be resolved boundary layer near the impeller and the shaft. Turbulence models used were k-epsilon and k-c omega models and their governing equations were also discretized by the Characteristic-Galerkin method that includes stabilizing terms as well as the momentum equation. Calculated results were compared with the experimental result. The doubleloop pattern in the r-z cross-section could be reproduced by both turbulence models, though with stronger circulation patterns. It was found that the k-w model could reproduce the Rankin's vortex qualitatively, while the k-E model could not even qualitatively.