A simulation of flow field and tracer homogenization was performed using the commercial CFD software FLUENT 6.1. The aim is to investigate the potential of CFD software to predict concentration distribution of added tracer in cylindrical vessels. The calculated results -dimensionless velocity profiles, power and pumping numbers, dimensionless concentration curves, and mixing times - were compared with experiments in stirred vessels. In Part I, the study was performed for vessels agitated by one or two impellers on a centric shaft. Two different impellers were used - a 6-bladed 45 degrees pitched blade turbine and a standard Rushton turbine. The standard k-epsilon turbulence model and multiple reference frames method were used for the simulations. The influence of the grid type was also investigated; three types of grid - a structured, unstructured and a special user-defined grid - were studied.