In this paper pulsatile blood flow through rigid circular tubes due to a sinusoidally varying pressure gradient is analyzed using a microcontinuum model of blood. A new boundary condition, which is in accord with experimental observations on blood flow in small rigid tubes, has been proposed to describe red blood cell rotations at a solid boundary. General solutions to the governing equations are obtained through application of consecutive Hankel and Laplace transforms. The steady pulsatile solutions for velocity and cell rotation are also given. The plasma viscosity, rotational viscosity, and rotational gradient coefficients are determined as functions of hematocrit from the experimental in vitro steady blood flow data of Bugliarello and Sevilla. These coefficients are then used to predict their pulsatile velocity profile data. Excellent agreement is obtained when non-Newtonian effects are absent.