jats:pIn the event of earthquake-induced liquefaction, structures with shallow foundations can suffer excessive settlement and rotation. In this paper, the rotational response of structures with shallow foundations resting on liquefiable layers with thickness equal to or smaller than the width of the foundation is examined through a series of dynamic centrifuge experiments. Moment–rotation backbone curves are extracted and the corresponding evolution of rocking stiffness with increasing rotation is depicted, in normalised terms. A stiffness attenuation relation is proposed, which can be used for simplified predictions of maximum and residual rotation using rotational spring and dashpot models. Two such examples are presented, one using an iterative, equivalent-linear rotational spring approximation, and one using Masing's rules for cyclic response, extended with Pyke's hypothesis.</jats:p>