There are many different mathematical models and solution techniques dealing with the blood flows. A twophase (liquid-solid) model solved by a perturbation method will be introduced. Effects of hematocrit, Reynolds number, area reduction, and different geometries of the stenotic channel are studied on the velocity, pressure gradient, and streamlines. The flow characteristics (velocity and pressure) give a great increase as the stenosis classified as a sever stenosis. It is found that, the stenosis geometry has a great effect on the pressure gradient in the axial direction, and also there is a change in velocity profile in each cross section of the geometry. The hematocrit has a noticed effect on the flow velocity and pressure gradient, in which as the hematocrit increases the maximum velocity decreases before the throat while it increased after that section.