The nonlinear dynamic behaviors of an elastic support hinged hinged uniform shallow arch with two torsional springs locating at two ends respectively under external excitation are investigated. Based on the control equation of elastic support shallow arch the multiple scale method was used for the perturbation analysis of internal resonances, and the averaging equation with its polar form was determined. The influence of the stiffness for elastic boundary, which has a one to one relationship to the corresponding coefficient in the averaging equation, can be reflected in the natural frequencies and mode shapes of arch structure via the characteristic equation. Then the 1:1 internal resonance between the lowest two modes was selected as studying object for numerical calculation. The analytical results show that there exist internal resonance forms for both cross and veer in the torsional elastic support shallow arch, further the two mode interaction induced by external excitation may lead to quasi periodic oscillation and chaotic motion when the systematical parameters are controlled in a certain range.