Finte element methods are developed for the initial distribution problems which contain the surge potential circuits of high voltage transformer windings. The initial distribution of surge voltages in transformer windings are useful to the work to a practical engineering basis. However, the conventional methods of analyzing them so far are much complicated for practical designs. In this paper, the ability to solve surge potential field problems underlies the development of descreting methods to a lodal capacitive distribution-coefficients for determing the surge voltage relationship among a set of transformer coils. A practical example-the modeling of an antioscillation shield coil winding and hisercap winding is used to illustrate and evaluate these methods.