The impact of multiple stenoses on the stream of a Casson fluid over a non-uniform pipe has been studied. Under the assumption of mild-stenosis, explicit solutions have been derived to calculate the flow resistance and shear-stress on the wall. The consequences of numerous relevant factors on these flow qualities are deliberated. It is experiential that the flow resistance declines with a change of radius in the plug region, where as the shear stress increases with the same. Further, both the above two flow characteristics upsurge with the elevations of the stenoses. The impacts of boundaries identified with statures of stenoses on shear-stress may support in improved recognition of the fluid mechanical viewpoints in stenotic stream area, which thusly would support in further comprehension of the advancement and improvement of 'Arteriosclerosis' in biological frameworks.