A Green function method is presented which enables computation of laminar flow of an incompressible Newtonian fluid in circular and annular pipes, subject to an arbitrary forcing periodic pressure gradient, in terms of Bessel functions. The response to a step change in pressure gradient in an annular pipe is presented. The method allows direct calculation of wall shear stress and flow rates generated by pulsed flows, which are of interest in fouling mitigation and cleaning-in-place systems. (c) 2005 Elsevier Ltd. All rights reserved.