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In this paper, a novel arch structure—circular box arch with sinusoidal corrugated webs (CBASCW)—is presented. Through the methods of theoretical derivation and finite element simulation, we studied its in-plane elastic buckling and in-plane elastoplastic stability. Through theoretical derivation, a shear stiffness formula of the arch section is determined, and the elastic buckling load when the arch is in pure compression state is proposed considering the shear deformation. We also introduced a simplified model, which can simulate the deformation and internal forces conveniently. The failure mode and global elastoplastic instability mechanism are investigated under uniformly distributed full-span radial load, uniformly distributed full-span vertical load, and uniformly distributed half-span vertical load. Furthermore, by introducing a regular slenderness ratio and stability coefficient, the stability curve of the arch under the state of pure compression is plotted. Subsequently, based on the stability curve and the numerical simulation results of a simplified model, a design formula for the stability bearing capacity is proposed for situations where global elastoplastic instability occurs. [ABSTRACT FROM AUTHOR]