For solving the two-dimension wheel/rail contact problem in statics, the gap element method was integrated into the vector form intrinsic finite element method to write a contact program (V-5-gap). A relationship between the contact stiffness and the normal load had been obtained for a wide load range, which was employed to determine the suitable contact stiffness. Taking the contact stiffness of 14 t axle load instead of gap elements, the corresponding conduct condition using V-5 was calculated. The result indicates that the contact pressure distribution of this model is consistent with those of ABAQUS and Hertz; Results under the axle loads of 10 t, 16 t and 20 t show that the maximum contact pressure and contact area changes reasonably with the normal load; and the contact pressure distribution calculated with V-5 method agrees well with Hertz’s result, which validates the contact model and the related contact stiffness searching approach.