Field observations of semi-taut mooring systems have shown severe trench development in front of suction caissons. Trenches extend back from where the chain emerges from the seabed under ambient mooring loads to relatively close to the caisson, and with depths approaching the padeye depth. To help understand the process, a Coupled Eulerian-Lagrangian (CEL) approach has been used to apply cyclic loading to a mooring chain system, treating the chain as a series of linked cylindrical elements and the soil as a strain-softening Tresca material. The chain extended through the soil into the water column, and cyclically changing boundary conditions were applied to the far-end of the chain to reflect a typical mooring layout and metocean conditions. In spite of rather idealized conditions, with loading restricted to the vertical plane of the chain and no consideration of hydrodynamic effects, a stable trench profile developed after only a few cycles of loading. The chain profile straightened during the cycles, with the section nearest to the padeye gradually cutting deeper into the soil and with the amplitude of cyclic motions of the chain, and hence tendency for a trench to form, increasing at shallower depths. The magnitude of soil resistance acting on the chain reduced by increasing cycles, with particularly low resistance in the zone where the trench was most developed. The long-term longitudinal profile of trenching was predicted based on the current modelling, and was found comparable to that inferred from field observations, even without consideration of hydrodynamic and out-of-plane effects.