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Abstract The stress balance within an ice shelf is key to the resistance, or buttressing, it can provide and in part controls the rate of ice discharge from the upstream ice sheet. Unconfined ice shelves are widely assumed to provide no buttressing. However, theory and laboratory-scale analogue experiments have shown that unconfined, floating viscous flows generate buttressing via hoop stresses. Hoop stress results from the viscous resistance to spreading perpendicular to the flow direction in a diverging flow. We build on theoretical work to explore the controls on the magnitude of hoop-stress buttressing, deducing that buttressing increases with increasing effective viscosity and increasing divergence. We use an idealised model calibrated to unconfined sections of Antarctic ice shelves and find that many shelves have low effective viscosity, most likely due to extensive damage resulting from high extensional stresses. Therefore, they are unable to sustain the large hoop stresses required to resist flow. Some ice shelves that are surrounded by sea ice year-round have a greater effective viscosity and can provide buttressing, suggesting that sea ice reduces fracturing. However, we find that most unconfined ice shelves provide insignificant buttressing today, even when hoop stresses are considered in the stress balance.