Red blood cell sedimentation has been used as a promising indicator of hematological diseases and disorders. However, to address several issues (i.e., syringe installation direction, blood on-off flow control, image-based quantification, and hemodilution) raised by the previous methods, it is necessary to devise a new method for the effective quantification of red blood cell sedimentation under a constant blood flow. In this study, the shear stress of a blood flow is estimated by analyzing an interface in a co-flowing channel to quantify the red blood cell sedimentation in blood syringes filled with blood (hematocrit = 50%). A red blood cell sedimentation index is newly suggested by analyzing the temporal variations in the shear stress. According to the experimental investigation, the sedimentation index tends to decrease at a higher flow rate. A higher level of hematocrit has a negative influence on the sedimentation index. As a performance demonstration of the present method, the red blood cell sedimentation processes of various test bloods were quantitatively compared in terms of the shear stress, image intensity, and sedimentation velocity. It was found that the proposed index provided a more than 10-fold increase in sensitivity over the previous method (i.e., image intensity). Additionally, it provided more consistent results than another conventional sedimentation method (sedimentation velocity). In conclusion, the present index can be effectively adopted to monitor the red blood cell sedimentation in a 10-min blood delivery.