We examine the applicability of three different non-Newtonian constitutive models (power-law, Casson, and Herschel-Bulkley models) to the determination of blood viscosity and yield stress with a scanning capillary-tube rheometer. For a Newtonian fluid (distilled water), all three models produced excellent viscosity results, and the measured values of the yield stress with each model were zero. For unadulterated human blood, the Casson and Herschel-Bulkley models produced much stronger shear-thinning viscosity results than the power-law model. The yield stress values for the human blood obtained with the Casson and Herschel-Bulkley models were 13.8 and 17.5 mPa, respectively. The two models showed a small discrepancy in the yield stress values, but with the current data analysis method for the scanning capillary-tube rheometer, the Casson model seemed to be more suitable in determining the yield stress of blood than the Herschel-Bulkley model.