If a Bingham fluid at rest undergoes a unidirectional flow through the sudden motion of one of its boundaries and the diffusion equation applies in the yielded region, it is shown that the yield surface cannot move with a finite speed into the unyielded material if both the velocity and its gradient are zero at the interface. Conversely, if the velocity is non-zero at the yield surface it can move with a finite speed. Applications of this result to the Rayleigh problem and a few shearing flows are made to show when the Bingham fluid behaves like a Newtonian fluid throughout the flow region or when the yield stress effects are important. (C) 2004 Elsevier B.V. All rights reserved.