Functional magnetic resonance imaging (FMRI) is a noninvasive method of imaging brain function in vivo. However, images produced in FMRI experiments are imperfect and contain several artifacts that contaminate the data. These artifacts include rigid-body motion effects, B0-field inhomogeneities, chemical shift, and eddy currents. To investigate these artifacts, with the eventual aim of minimizing or removing them completely, a computational model of the FMR image acquisition process was built that can simulate all of the above-mentioned artifacts. This paper gives an overview of the development of the FMRI simulator. The simulator uses the Bloch equations together with a geometric definition of the object (brain) and a varying T2* model for the BOLD activations. Furthermore, it simulates rigid-body motion of the object by solving Bloch equations for given motion parameters that are defined for an object moving continuously in time, including during the read-out period, which is a novel approach in the area of MRI computer simulations. With this approach it is possible, in a controlled and precise way, to simulate the full effects of various rigid-body motion artifacts in FMRI data (e.g. spin-history effects, B0-motion interaction, and within-scan motion blurring) and therefore formulate and test algorithms for their reduction.