Numerous experiments have been performed to show that for oscillatory blood flow in a tube, sufficiently large volume flow rate amplitudes will break up blood aggregates leading to a loss of elasticity and to a response by the pressure gradient oscillations typical of those of a viscous fluid in inertial flow [G.B. Thurston, Elastic effects in pulsatile blood flow, Microvasc. Res. 9 (1975), 145-157]. In this paper we use the non-homogeneous blood model developed in Part I of this work [M. Moyers-Gonzalez, R.G. Owens, J. Fang, A non-homogeneous constitutive model for human blood. Part I. Model derivation and steady flow, submitted for publication] to simulate blood undergoing oscillatory flow and, in particular, to examine the behaviour of the components of the pressure gradient that are in phase and pi/2 out of phase with the volume flow rate, as the volume flow rate amplitude is varied. Excellent agreement is found with experimental data for a tube of radius 430 mu m. An improvement in the predictions compared to those of an earlier homogeneous model [J. Fang, R.G. Owens, Numerical simulations of pulsatile blood flow using a new constitutive model, Biorheology 43 (2006) 637-660] is evidenced. We also seek to relate the macroscopic blood behaviour in different size tubes and at two different angular frequencies to the aggregate properties such as the average aggregate size and the cell number density. (C) 2008 Elsevier B.V. All rights reserved.