The non-ideal boundary conditions (neither fixed nor hinged) of arch structure were considered as an elastic constraint with certain stiffness in different directions, and the nonlinear equilibrium equation was determined by using deformation geometric relation and energy variation principle. A circular arch under radial uniform load was taken as an example to establish the relationships between the external load and the internal force, and the radial displacement. By defining the shallowness and critical constraint stiffness, the snap-through buckling and bifurcation buckling were studied and the occurrence condition and distribution range were investigated. The buckling path and critical buckling load in the proposed method were in good agreement with the results from the finite element method. And the numerical method was used to study the buckling path and critical buckling load for different stiffness of elastic constraint. The results show that the critical shallowness and the critical constraint stiffness play a fundamental role in the buckling mode and critical buckling load for circular arch.