A transport-based, three-dimensional numerical modeling approach has been developed to simulate chemical mechanical polishing processes occurring in microelectronic materials processing. A unique aspect of this model is that the detailed morphology of the slurry flow domain between thr wafer and polishing pad is approximated with a regularly updated sequence of geometries evenly positioned along the polishing orbit. Additionally, the modeling approach allows the use of any constitutive relationship for the rheological behavior of the polishing slurry. The local polishing rate is taken to be proportional to the local hydrodyanmic shear stress generated on the to-be-polished wafer surface. To illustrate the modeling approach, the development of planarity Juring polishing of a prototypical 3 x 3 array of square roughness elements was simulated. The rheology of the polishing medium was described as a power-law fluid with a Newtonian plateau, which is appropriate for an aqueous slurry of colloidal silica. Two modes of pad-to-wafer tracking during polishing are discussed. Modeling results show good agreement with typical experimental data.