The flow through a centrifugal compressor rotor was calculated using the quasi-3-dimensional and fully 3-dimensional Navier-Stokes solution methods. The calculated results, obtained during the development of the computer codes for both methods are discussed. In the inviscid quasi 3-dimensional analysis, stream function formulation was used for the blade to blade (B-B) plane calculations, and the streamline curvature method was used for the meridional (H-S) plane calculations. In the viscous 3-dimensional flow analysis, a control volume method based on a general rotating curvilinear coordinate system was used to solve the time-averaged Navier-Stokes equations, and a standard k-.epsilon. model was used to obtain eddy viscosity. The quasi-3-dimensional analysis reasonably predicts the pressure distributions and requires much less computation time in the region where viscous effects are not strong; however, it fails to predict velocity field and loss mechanism through the impeller passage. The viscous 3-dimensional flow analysis shows reasonable pressure distributions and typical jet-wake flow field through the impeller passage. Secondary flow and total pressure distributions on cross-sectional planes explain the loss mechanisms through the impeller.