The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress, and the power law index on the velocity distribution, streamline pattern, and wall shear stress. On the basis of the derived analytical expressions, extensive numerical calculations have been made. The study reveals that velocity of blood and wall shear stress are appreciably affected due to the nonuniform geometry of blood vessels. They are also highly sensitive to the magnitude of the amplitude ratio and the value of the fluid index.