The multidimensional partition model, which combines the k-space description of magnetic resonance imaging pulse sequences with a partition concept, has been developed to model flow-related effects. A partition represents the magnetization created due to excitation by a given radiofrequency pulse. In the present model, it is visualized as a set of parameters rather than a vector sum taken over a collection of spins. The phase dispersion due to velocity and higher orders of motion is described by adding new dimensions to the three spatial k-space dimensions. The computer implementation of the model is capable of simulating the outcome from pulse sequences used in clinical routines and it does not need assumptions regarding pulse sequence parameters. Furthermore, flow-induced effects due to phase dispersion, caused by movements in a magnetic field gradient, as well as the inflow of unsaturated spins, are handled by the model. Constant or varying (pulsatile) flow velocity may be assigned together with different velocity profiles (e.g., plug flow, laminar flow) over a simulated vessel. The model makes it possible to simulate images of an object containing vessels with pulsatile laminar flow pattern, scanned using a three-dimensional angiography pulse sequence, in <10 min on a Pentium-based PC system. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 115–127, 1999