In the study of blood rheology in vivo,the author found that it is actually wrong to use the Casson fluid model to describe the flow state of blood in vivo.The purpose of this study is to correct this theoretical error,which has existed for nearly 40 years,and at the same time to maintain the correct theory obtained by predecessors and authors in vivo blood flow regimes.In this paper,we use theoretical research methods to demonstrate the rele-vant fluid dynamics,hemodynamics,blood rheology theories and the actual blood flow in vivo,and reveal that there is no Casson fluid model in the systemic blood vessels,and the aggregation of red blood cells is not the essential mechanism of the Casson fluid model in the systemic blood vessels.The artery blood flow pattern in vivo is laminar flow that varies periodically with the heart rate,except for the specific areas of the arteries and veins,in the veins it can be approximated as steady flow.