Abstract: The effects of non--linear magnetic field involve a set of non--linear differen-tial equations, which is difficult to be solved analytically. A computer simula-tion method is described. Taking the advantage of Monte Carlo technique.it can be applied to determine the tolerance of magnet field, andincorporated with magnet measurment data, the tracking study can be carried outin a imperfect ring. The method has successfully found its application in theBEPC magnet tolerance study as well as field quality evaluation of the magnetprototypes.