Dynamic shimming in multi-slice imaging aims to achieve optimal magnetic field homogeneity by updating the shim coil currents for each slice in real time. Dynamic shimming may reduce the signal loss and geometric distortion caused by magnetic susceptibility variations between tissues and is likely to be valuable for fast T2*-sensitive imaging techniques like EPI. A computer simulation of dynamic shimming using real image data has been developed to demonstrate the effectiveness of higher order dynamic shimming for echo planar imaging at high magnetic field, and to investigate the potential benefits of different orders of shim coil. Geometric distortions and signal intensities for different degrees of dynamic shimming were simulated and the results are compared with the images obtained with a conventional shimming technique. These results demonstrate the effectiveness, necessity and difficulty of high order dynamic shimming.