In this present paper, we studied about the flow of Herschel-Bulkley fluid through an overlapping stenosis. Most of the people in today’s world are much worried about the health-related issues. One among the many diseases that is causing worry to the people is the cardiovascular diseases. The entire human body is controlled by the heart and the blood vessels, which are important in transporting the blood from heart to various parts of body and vice versa, due to the pressure variation developed when the heart extracts and contracts periodically. One of the most common cardiovascular diseases is atherosclerosis that occurs due to the improper flow of blood in human body. In this view, as blood flow is playing an important role in diseases related with heart, many researchers are showing interest in this area. Atherosclerosis is a cardiovascular disease that is caused due to an aberrant growth formed in lumen of an artery. It generally occurs when the human body gets habituated to unhealthy habits such as chewing tobacco, lack of exercises etc. Owing to this the characteristics of blood such as pressure distribution, shear stress on the wall, flow resistance etc. gets affected.