Abstract: Acetylsalicylic acid is a salicylate drug which is used to decrease viscosity of blood by diluting the blood which ultimately decreases the blood pressure of the patients. The effects of peripheral layer on blood flow characteristics due to the presence of a mild stenosis are also studied in this study. A two Fluid Model for blood flow through abnormally constricted stenosed artery has been developed. The model consists of a core region of suspension of all erythrocytes assumed to be Bingham Plastic Fluid Model, to find the effects of peripheral-layer viscosity and a peripheral plasma layer free from cells of any kind of Newtonian fluid is considered. It is shown that the magnitudes of the flow characteristics significantly increase with stenosis shape parameter and the peripheral layer causes marked reduction in the magnitudes of the flow characteristics. Physiological relevance and the influence of various parameters are discussed.