Previous studies of freshwater lenses in saline aquifers adjoining gaining rivers (“riparian lenses”) have so far considered only rivers that fully penetrate the aquifer, whereas in most cases, rivers are only partially penetrating. This paper presents a new methodology for obtaining the saltwater discharge and the shape of a steady-state, non-disperive riparian lens, where the river is partially penetrating, combining two previous analytical solutions. The resulting analytical solution is compared to numerical modelling results to assess assumptions and the methodology adopted to approximate the “turning effect”, which is the change in groundwater flow direction (horizontal to vertical) near the partially penetrating river. A range of conditions are analysed, constrained by parameters adopted previously for River Murray floodplains (Australia). Consistency between analytical and numerical results highlight the capability of the proposed analytical solution to predict the riparian lens geometry and saltwater discharge into partially penetrating rivers. The sensitivity analysis indicates that larger riparian lenses are produced adjacent to the deeper and wider rivers, as expected. The change in width or depth of the river has more influence on the saltwater discharge and the horizontal extent of the riparian lens (and less effect on the vertical extent of the lens adjacent to the river) for shallower and narrower rivers. This research highlights the utility of the new method and demonstrates that the assumption of a fully penetrating river likely leads to significant overestimation of the saltwater discharge to the river and the riparian lens horizontal extent and vertical depth.