Abstract: The performance of a Quadrupole Mass Spectrometer is affected closely by its quadrupole field. The ideal field should be a hyperbolic field. In fact, the round electrodes have been used in many instrument, because making a electrode with a hyperbolic cross section is very difficult. In the paper, besides the difference between both cases has been studied, the other shape electrode structure has been analyzed to look for the cause which affect the distribution of the electronic potential for instructing the manufacture of the electrode poles. These electrodes are the circle arctangent pole and the hyperbolic-tangent pole with some of different tangent slopes. The conclusion is that the distribution of a field is determined by the electrode figure in the center part against the field.The effects of the circle shield with zero potential has been considered. If the rate between the radius of the shield electrode and the radius of the quadrupole field is larger than 3.54, the variation of the field is very little with the radius.The influence from both errors of electrode figure and position are calculated in the paper. The effect of the position error is more than that of the figure error. In addition, the effects of the positive and the negetive of the errors is approximate equal.