We compare two approaches to numerical estimation of mechanical hemolysis in a simplified blood pump model. The stress-based model relies on the instantaneous shear stress in the blood flow, whereas the strain-based model uses an additional tensor equation to relate distortion of red blood cells to a shear stress measure. We use the newly proposed least-squares finite element method (LSFEM) to prevent negative concentration fields and show a stable and volume preserving LSFEM for the tensor equation. Application of both models to a simplified centrifugal blood pump at three different operating conditions shows that the stress-based model overestimates the rate of hemolysis. The strain-based model is found to deliver lower hemolysis rates because it incorporates a more detailed description of biophysical phenomena into the simulation process. Copyright © 2013 John Wiley & Sons, Ltd.