Abstract: In view of dilatancy after rock mass enters the plastic state induced by excavation and the situation that analytic solution for non-circular tunnel surrounding rock response status still can not be solved, the constitutive relation for the surrounding rock that can reflect the dilatancy is selected, and then, the response characteristic functions of the surrounding rock of tunnel for all kinds of section forms after excavation are established. First, numerical model for various cross-section shapes of tunnel excavation is established and analyzed, and the results are used to draw the surrounding rock after excavation, such as response curves of common tunnel sections of rectangle, straight wall arch and curved wall arch. Then, under the same conditions, the elastic-plastic response characteristic curves of cross-sections of rectangle, straight wall and curved wall arch under 5 kinds of equivalent circular section method are drawn based on the analytical method for circular tunnel proposed by Duncan-Fama considering dilatancy. Finally, the closeness degree between the analytical and numerical simulation curves, is compared in order to obtain the equivalent circular method corresponding to the closest analytical curve. It may provide convenienle for the establishment of response characteristic analytic function for dilatant surrounding rock of tunnel with arbitrary cross-section.