Susceptibility weighted imaging (SWI) uses apparent phase contrast to enhance the contrast-to-noise ratio (CNR) in the magnitude image. In theory, the apparent phase will depend on the aspect ratio when both venous blood and parenchyma occupy the same voxel. To demonstrate the maximal expected effect of the external field from a vein, we model the vein as an infinitely long cylinder perpendicular to the main magnetic field. The results show that the apparent phase of a voxel in the image is a function of resolution, vessel size and, to a lesser degree, vessel center within the voxel. The simulations explain why a negative-phase mask has worked in SWI processing of high-resolution images collected in the transverse direction, despite the expected positive-phase behavior for vessels perpendicular to the main field. The predicted phase behavior from the simulations is in good agreement with that observed from human brain datasets.