A numerical method for obtaining the vibrating sample magnetometer (VSM) sensitivity functions due to a uniformly magnetized sample in the shape of ellipsoid, cuboid or cylinder, and then calculating the induced voltage in a VSM detection coil systems is presented. The induced voltage, which depends on the equilibrium position and amplitude of the sample in three‐dimensional space, and depends on the geometric parameters of both sample and detection coils, is calculated from the viewpoint of magnetic charges. This numerical method is more accurate than others, which use dipole moment approximation without taking into consideration the sample shape and size. By using this method, the induced voltage, for which the shape and size effects of the sample must be taken into account, can be calculated if there is knowledge of geometric parameters of the sample and coils. The formulas for calculating the correction coefficient are also given for samples whose shape errors should be considered. Our results provide rigorous theoretical guidance for the exhaustive study of the VSM working principle, for accurate measurement of the sample magnetic moment, and for optimum design of configuration, position, and orientation of VSM pickup coils. ©1996 American Institute of Physics.