The Newtonian Poiseuille flow is considered for various geometries, under the assumption that wall slip occurs above a critical value of the wall shear stress known as, the slip yield stress. In the axisymmetric and planar cases, there are two flow regimes defined by a critical value of the pressure gradient above which slip occurs. Two critical pressure gradients characterise the annular and rectangular Poiseuille flows. Below the first critical value no-slip occurs while above the second-one, slip occurs at all walls. In the intermediate regime for the annular problem, slip occurs only at the inner-wall, while for the rectangular problem, there are two intermediate regimes for which there are no analytical solutions. In the first regime slip occurs only in the middle sections of the wider walls and in the second-one partial slip also occurs along the narrower walls. Analytical solutions of all flow problems (with the exception of the two intermediate regimes of the rectangular Poiseuille case) are derived and discussed. (C) 2013 Elsevier BM. All rights reserved.