Floating offshore wind turbines are the subject of increasing interest, as a response to growing societal demands for renewable energy. They enable the harnessing of wind power further away from the coast in larger and deeper offshore fields where fixed structures may not be practical, which in turn imposes challenges for their mooring systems. This paper explores the finite element modelling of suction caisson foundations in tension leg structures under conditions of cyclic loading. It emphasises the application of a novel elasto-plastic constitutive framework with nonlinear kinematic hardening, formulated to mimic the operation of hypoplastic or general plasticity models. It further explores the effect of permeability in coupled analyses involving granular seabed deposits, as well as general interaction of the soil with skirted foundations.