Functional Magnetic Resonance Imaging (fMRI) is a non-invasive method of imaging brain function in-vivo. However, images produced by fMRI scanners are not perfect and contain several artifacts which contaminate the data. These artifacts include motion effects, RF intensity inhomogeneity, unwanted physiological signals related to the cardiac and respiratory cycles, etc. To investigate these artifacts, with the eventual aim of minimising or removing them completely, we have built a computational model of the image acquisition process. Our model simulates echo-planar imaging and uses the fundamental Bloch equations which describe the time-dependent behaviour of magnetization vector M in the presence of an applied RF field, together with a geometric definition of the object (brain) and the rigid-body motion of this object. In order to make the model more realistic we have also included static field inhomogenities including those due to magnetic susceptibility, errors in the applied field and chemical shift.