Time-of-flight magnetic resonance (MR) angiography is currently limited in the evaluation of arterial stenoses by flow-induced signal loss. This signal loss has been attributed to phase dispersion and to phase misregistration. We have developed a fluid mechanics model of 2D time-of-flight MR angiograms to study the amount of signal loss caused by random turbulence. The simulations were created by stochastic analysis of particle pathlines determined by computational fluid dynamics for turbulent flow. The images obtained by the model compare well to actual MR images of flow in stenoses. By selectively removing the random turbulent motion in the simulation, it can be seen that random phase dispersion is the dominant mechanism of signal loss. Phase misregistration and mean flow phase dispersion act as secondary effects. The MR simulation model recreates accurately the variation of signal loss over a range of echo times. The model can be used further to explore and design new pulse sequences. For example, the current study showed that high slew rate gradient waveforms can significantly reduce poststenotic signal loss. In conclusion, computational modeling of MR angiography can be a useful approach for the analysis of MRA signal loss and the design of improved pulse sequences.