A method is proposed to study the steady blood constitutive equation (BCE). With the method several BCEs are tested and Quemada, Bi-exponent and K-L equations are found to be well in agreement with the hemorheological characteristics of human and canine blood and these equations may be well used in hemorheology and hemodynamics. In addition, the potential clinical applications of some blood constitutive parameters (BCPs) are discussed. It is found that the hematocrit can significantly affect the BCPs: K(A) = alpha2/alpha1, Q(A) = eta0/eta(infinity), R(A) = etaA/eta(e) - 1, which means relative viscosities and they may be related to RBC aggregative level. Moreover, we also show that the parameters are related to the RBC aggregative strength and level.