This paper takes leaning-type arch ribs system as research subject. And based on the Ritz method, the analytic solution of the lateral buckling critical load of leaning-type arch ribs system under the arch springing hinged boundary condition is derived. Compared with the result obtained from FEM, it is verified that the lateral buckling critical load analytic solution presented in this paper is accurate enough. On that basis, the effect of boundary condition on the lateral bucking critical load of leaning-type arch rib system is analyzed. It is shown that the lateral stability of the leaning-type arch rib system under arch springing clamped boundary condition is much better than the one under hinged boundary condition. And the former’s lateral bucking critical load is 2.13~2.49 times as large as the latter’s. Stable arch inclined angle growing, the leaning-type arch rib system’s lateral bucking critical load increases effectively. But its amplitude under hinged boundary condition increase larger.