In this theoretical investigation, a mathematical model is developed to study the effect of multiple stenoses on flow characteristics of streaming blood through the atherosclerotic artery. The Bingham plastic fluid model of blood has been utilized in the study to represent the non-Newtonian character of blood. The geometry of the asymmetric shape of the stenosis assumed to be manifested in the arterial segment is given due consideration in the analysis. An extensive quantitative analysis is performed through numerical computations on flow resistance, wall shear stress and their variations are presented graphically for different stenotic and other rheological parameters. It is observed that the stenotic and physical parameters have considerable effect in the flow behaviour. Some important observations having medical interest on the flow of blood in the stenosed arteries are presented. The investigation bears the potential to explore a variety of information regarding some phenomenological aspects of the physiological problem. The output of the investigation may provide supplementary support to the physician in the treatment of the fatal disease.