The use of spatial presaturation to suppress the signal, and therefore also the artifacts, from flowing blood has become an important tool in the arsenal of techniques to suppress pulsatile flow artifacts in magnetic resonance images. However, a detailed theoretical analysis of the behavior of these flow artifact suppression pulses and of the important aspects of implementing suppression pulses in combination with particular imaging sequences has yet to be presented. In this paper we present a general theoretical framework to describe the flow artifact suppression technique. This analysis addresses the following four major issues: (1) the spin washout characteristics of the imaging sequence, (2) the interference between the flow signal suppression pulses and the imaging sequence, (3) the flow velocity range for a single application of the suppression pulse, and (4) the total flow velocity range for a suppression pulse repeated with a constant time interval between applications of the pulse. The predictions of our theoretical model are confirmed by experimental measurements made with stationary and flow phantoms. The results of this investigation provide guidelines for the design of flow artifact suppression pulse sequences and, in addition, should aid in the future development and refinement of the spatial presaturation technique as applied to flow signal suppression.