PURPOSE: Simulation of MR flow motion is of high interest for the study of flow artifacts formation and angiographic acquisitions processes. Though, currently, most of advanced MRI simulators do not include this option and are specialized in static tissues imaging. This work was carried out to expand the possibilities of one of those softwares to the general field of MR spin flow simulation. THEORY AND METHODS: An extension of JEMRIS, one of the most prevalent high performance open-source softwares for MRI simulation to date, is presented. Implementing a Lagrangian description of individual spins motion in the code makes possible to simulate any MR experience, including both static tissues and arbitrarily complex flow data from Computational Fluid Dynamics (CFD). RESULTS: The e ciency of this approach is illustrated with a common flow artifact (misregistration artifact) and tested with the main three angiographic methods (phase contrast velocimetry, time-of-flight sequence and contrast-enhanced imaging). A realistic simulation of MRA on a full cerebral venous network is then provided. CONCLUSION: This framework provides an e cient and versatile tool for the simulation of any MRI experience including physiological fluids with arbitrarily complex flow motion.