At several localities around the world, thrust belts have developed on both sides of oceanic island arcs (e.g., Java-Timor, Panama, Vanuatu, and the northeastern Caribbean). In these localities, the overall vergence of the backarc thrust belt is opposite to that of the forearc thrust belt. For example, in the northeastern Caribbean, a north-verging accretionary prism lies to the north of the Eastern Greater Antilles arc (Hispaniola and Puerto Rico), whereas a south-verging thrust belt called the Muertos thrust belt lies to the south. Researchers have attributed such bivergent geometry to several processes, including: reversal of subduction polarity; subduction-driven mantle flow; stress transmission across the arc; gravitational spreading of the arc; and magmatic inflation within the arc. New observations of deformational features in the Muertos thrust belt and of fault geometries produced in sandbox kinematic models, along with examination of published studies of island arcs, lead to the conclusion that the bivergence of thrusting in island arcs can develop without reversal of subduction polarity, without subarc mantle flow, and without magmatic inflation. We suggest that the Eastern Greater Antilles arc and comparable arcs are simply crustal-scale bivergent (or “doubly vergent”) thrust wedges formed during unidirectional subduction. Sandbox kinematic modeling suggests, in addition, that a broad retrowedge containing an imbricate fan of thrusts develops only where the arc behaves relatively rigidly. In such cases, the arc acts as a backstop that transmits compressive stress into the backarc region. Further, modeling shows that when arcs behave as rigid blocks, the strike-slip component of oblique convergence is accommodated entirely within the prowedge and the arc—the retrowedge hosts only dip-slip faulting (“frontal thrusting”). The existence of large retrowedges and the distribution of faulting in an island arc may, therefore, be evidence that the arc is relatively rigid. The rigidity of an island arc may arise from its mafic composition and has implications for seismic-hazard analysis.