The coupled poro-mechanical behaviour of geologic-fluid systems is fundamental to numerous processes in structural geology, seismology and geotechnics but is frequently overlooked in hydrogeology. Substantial poro-mechanical influences on groundwater head have recently been highlighted in the Bengal Aquifer System, however, driven by terrestrial water loading across the Ganges-Brahmaputra-Meghna floodplains. Groundwater management in this strategically important fluvio-deltaic aquifer, the largest in south Asia, requires a coupled hydro-mechanical approach which acknowledges poro-elasticity. We present a simple partially-coupled, one-dimensional poro-elastic model of the Bengal Aquifer System, and explore the poro-mechanical responses of the aquifer to surface boundary conditions representing hydraulic head and mechanical load under three modes of terrestrial water variation. The characteristic responses, shown as amplitude and phase of hydraulic head in depth profile and of ground surface deflection, demonstrate (i) the limits to using water levels in piezometers to indicate groundwater recharge, as conventionally applied in groundwater resources management; (ii) the conditions under which piezometer water levels respond primarily to changes in the mass of terrestrial water storage, as applied in geological weighing lysimetry; (iii) the relationship of ground surface vertical deflection to changes in groundwater storage; and (iv) errors of attribution that could result from ignoring the poroelastic behaviour of the aquifer. These concepts are illustrated through application of the partially-coupled model to interpret multi-level piezometer data at two sites in southern Bangladesh. There is a need for further research into the coupled responses of the aquifer due to more complex forms of surface loading, particularly from rivers.