This article is concerned with the analysis of a dusty model for the axi-symmetric flow of blood through coaxial tubes such that the outer tube with an axially nonsymmetreic but radially symmetric mild stenosis and the inner tube have a balloon (assumed that is axi-symmetric in nature). The mild stenosis approximation is used to solve the problem. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also employed to study the effect of the volume fraction density of the particles C, the maximum height attained by the balloon 2, the radius of the inner tube, which keeps the balloon in position , and the axial displacement of the balloon xd. Flow parameters such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed numerically for different shape parameters n, C, 2, , and xd. It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape n and the axial displacement of the balloon xd, while the resistance to flow increases with the volume fraction density of the particles C, the radius of the inner tube, which keeps the balloon in position , and the maximum height attained by the balloon 2. The magnitudes of the resistance to flow are higher in the case of a dusty fluid model than in the case of a Newtonian fluid model. The wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis possess a character similar to the resistance to flow with respect to C, 2, , and xd. Finally, the effect of the volume fraction density of the particles C, 2, and xd on the velocity profile are discussed.