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Dissipative effects due to hydrodynamic interactions between red cells are studied by describing blood rheology using polar fluid theory. Appropriate ranges of values for the two fluid substructure parameters are discussed. The problem of oscillatory motion of the fluid in a thin walled elastic tube is solved. The phase velocity ratio and transmission per wavelength are determined, as are other details of the motion of the fluid. It is found that hydrodynamic interactions between red cells significantly reduce the transmission per wavelength. Further, the discrepancy in phase between calculated and observed flow in the femoral artery that results from Womersley’s [Phil. Mag.46, 199, 1955] theory appears to vanish entirely when one uses the present analysis to account for dissipative effects of cell interactions.