Turbulent flows around tube banks and in the diffuser were studied using a non-orthogonal boundary fitted coordinate system and the modified K-.epsilon. turbulence model. In these cases, many problems emerge which stem from the geometrical complexity of the flow domain and the physical complexity of turbulent flow itself. To treat the complex geometry, governing equations were reformulated in a non-orthogonal coordinate system with Cartesian velocity components and discretised by the finite volume method with a non-staggered variable arrangement. The modified K-.epsilon. model of Hanjalic and Launer was applied to solve above two cases under the condition of strong and mild pressure gradient. The results using the modified K-.epsilon. model results in both test cases.