Centrifuge model tests are used to examine the dynamic response of structures supported by shallow foundations on soft clay reinforced by soil-cement grids. The centrifuge models involved a deep, lightly over-consolidated clay profile with three different soil-cement grid configurations. Structures on square shallow foundations were located over the central part of each soil-cement grid system. The models were subjected to multiple shaking events with peak base accelerations ranging from 0.006 to 0.546 g. The recorded responses of the structures and reinforced soil profiles were used to define the dynamic moment-rotation-settlement responses of the shallow foundations across the range of imposed shaking intensities. While the soil-cement grids were effective at controlling foundation settlements in most cases, the more significant foundation settlements which developed for the weakest soil-cement grid configuration under the stronger shaking intensities produced a rocking response of the structure and caused extensive crushing of the soil-cement below the edges of the shallow foundations. Analysis methods for predicting the demands imposed on the soil-cement grids by the inertial loads from the overlying structures and the kinematic loading from the soil profile's dynamic response are evaluated for consistency with the observed damage patterns. The experimental data have been archived and provide a basis for future studies to evaluate numerical and design analysis methods.