In small blood vessels, such as venules, arterioles, and the smaller arteries, the blood flow exhibits solid-like behavior in regions where the shear stress is less than the yield value. The Casson flow equation, originally designed to represent the movement of pigment/oil suspensions such as printing ink, is a fairly realistic model for the flow of blood in venules and arterioles. For such vessels, the frequency parameter is very small, of the order of 10 (exp -2) for a 0.4mm-diameter arteriole. To determine the flow of a Casson fluid under periodic pressure gradient, asymptotic expansions were applied in the square of the frequency parameter, and the simplified equations were then solved numerically. First-order inertial corrections were found to be negligible. The quasi-steady theory is a good approximation of reality, if the yield plane shifts as the pressure changes. (Presented at the 6th Conference of the European Microcirculation Society, Aalborg, Denmark, June 1970.) 13 pp. Ref.