An interesting feature of an island-arc chain is a cusp of the arcuate trench at the arc-arc junction where the Wadati-Benioff zone and the volcanic front are also sharpened landward. This cusp has been interpreted as a result of the collision of an aseismic ridge with the trench. We propose a different mechanism, intrinsic to the subduction of a spherical shell of lithosphere. When the spherical lithosphere is bent inward at a subduction zone, buckling takes place, and the slab is deformed into a wavy configuration making the trench chainlike. We analyzed this buckling phenomenon of spherical shells by a finite element method, wliich has been developed in the fields of architecture and civil engineering. Our calculations show that the lithospheric shell buckles with a wavelength roughly consistent with the length of one unit of island arcs (i.e., the distance between the two neighboring junctions). The resultant undulation is not purely sinusoidal, but is a succession of arcs with cusps in between, very similar to the shape of the actual arc-trench system in the world. This agreement strongly suggests that the arcuateness of the trenches and the cuspate form of their junctions are the manifestation of buckling of the spherical lithosphere, although the collision of seamounts and aseismic ridges against the trench may promote the initiation of buckling.