Abstract This paper describes the development of a framework to predict scour and undermining around squat, shallowly embedded structures under time-varying currents. Squat structures, with height equal to or smaller than their horizontal dimensions, are frequently employed offshore for a range of purposes, including pipeline and cable infrastructure, offshore substations, and innovative applications like offshore data centers and artificial reefs. These structures typically feature a rectangular base with a seabed-embedded skirt to increase the geotechnical capacity of the foundation and guard against the risk of local scour compromising the foundation. To investigate scour development at these structures, and to develop a framework to predict scour and undermining, experiments have been conducted using a generic squat structure with a shallow skirt foundation placed on a sandy bed within uniform grain size. Initially four experiments with different unidirectional currents were performed. For each of these experiments scour was initiated by the flow at the corners of the structure and scour holes developed, eventually leading to the undermining of the structure. The flow conditions were run until an equilibrium profile was observed, and the equilibrium scour depth, the equilibrium extent of undermining, and the associated timescales of these processes were obtained. These values were then used in a STEP model (Scour Time Evolution Predictor) scheme to predict how scour would evolve in time-varying currents. Comparisons of the STEP model with an additional experiment simulating a time-varying unidirectional current show that the time-history of scour depth, extent and the undermining area can be predicted reasonably well, indicating that the STEP model can be applied to scour assessment in time-varying currents.