The steady plane Poiseuille flow of a liquid crystalline material is studied using the Leslie-Ericksen continuum theory. The mean molecular orientation is assumed to be confined to the plane of shear. In the first part, the flow of a flow-aligning nematic was investigated; in this second part that of a tumbling nematic is studied. In the case of an isothermal plane Poiseuille flow it is shown numerically that multiple solutions of the flow equations exist for a prescribed pressure gradient. The resulting orientation and velocity profiles are not necessarily symmetric with respect to the midplane of the channel. A temperature difference across the channel causes the flow to become strongly asymmetric and also in this case the solution of the flow equations is not unique for a prescribed pressure gradient.