Abstract: The successful use of centrifugal pumps as temporary cardiac assist devices strongly depends on their degree of blood trauma. The mechanical stress loading experienced by cellular components on their passage through the pump is a major cause of blood trauma. Prediction of the mechanical stresses will assist optimization of pump design to minimize hemolysis and platelet activation. As a theoretical approach to this task, the determination of the complete three-dimensional (3D) flow field including all regions of high shear stress is therefore required. A computational fluid dynamics (CFD) software package, TASCflow, was used to model flow within a commercially available pump, the Aries Medical Iso-flow Pump. This pump was selected in order to demonstrate the ability of the CFD software to handle complex impeller geometries. A turbulence model was included, and the Newtonian as well as the Reynolds stress tensor calculated for each nodal point. A novel aspect was the assignment of scalar stress values to streaklines representing particle paths through the pump. Scalar stress values were obtained by formulating a theory that enables the comparison of a three-dimensional state of stress with a uniaxial stress as applied in all mechanical blood damage tests. Stress loading-time functions for fluid particles passing inlet, impeller, and outlet domains of the pump were obtained. These showed that particles undergo a complex, irregularly fluctuating stress loading. Future blood damage theories would have to consider an unsteady stress loading regime that realistically reflects the flow conditions occurring within the pump. Validation of the pump flow modeling is demonstrated with pressure head discrepancies predicted to be within 15% of measured values.