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Tolerable mobility of subsea foundations and pipelines supporting offshore oil and gas developments has recently become an accepted design concept. It enables a smaller foundation footprint and so is a potential cost-saving alternative to conventionally engineered ‘fixed’ seabed foundations. Dominant sources of loading on subsea infrastructure arise from connection misalignment or thermal and pressure-induced expansion, and these are reduced if the structure is permitted to displace while ensuring that additional loading is not induced by excessive settlements. A sound prediction of the resulting sliding response will provide a robust design basis for mobile subsea infrastructure. This paper presents a theoretical model based on critical state soil mechanics to predict the performance of a subsea installation that is founded on soft, normally consolidated or lightly overconsolidated soil, and subjected to intermittent horizontal sliding movements. The framework is validated against centrifuge test results and is shown to capture the essential elements of the soil–structure interaction, which include: (a) the changing soil strength from cycles of sliding and pore pressure generation; (b) the regain in strength due to dissipation of excess pore pressure (consolidation); and (c) the soil contraction and consequent settlement of the foundation caused by the consolidation process.