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Flowing blood is responsible for a number of complex effects on clinical magnetic resonance (MR) images. To help elucidate these effects, a computer model of a conventional multislice spin-echo pulse sequence was developed. Using TR, TE, and direction of slice acquisition, the model calculates and plots a profile of MR signal intensity vs. z-axis velocity. The model predicts complex profiles with multiple segments of MR signal loss depending on TR, TE, direction of flow, sequence and timing of slice excitation, and slice location relative to adjacent slices. Model predictions were verified by imaging a bulk-flow phantom, consisting of a rotating cylinder filled with a manganese chloride solution with T1=840 msec and characterized by a velocity-gradient resolution of 0.23 cm/sec/pixel. In conventional spin-echo MRI of medium and large vessels using body coils, in which the velocity gradients exceed 2-5 cm/sec/pixel, most of the flow artifacts are averaged and are difficult to appreciate. However, bright crescents or rings of MR signal occasionally are seen in the inferior vena cava and portal vein, which the model is invoked to explain. The bulk-flow phantom will find use as a tool for calibrating flow-sensitive pulse sequences when these become widely available.