We hypothesize that onshore saline groundwater in delta systems may have resulted from rapid shoreline progradation during the Holocene. To explore this hypothesis, we develop a model for the transport of saline groundwater in a shore-normal longitudinal cross-section of an evolving ocean margin. The transport model uses a control volume finite element model (CVFEM), where the mesh of node points evolves with the changing aquifer geometry while enforcing local mass balance around each node. The progradation of the shoreline and evolution of the aquifer geometry is represented by assuming the shoreline advances at a prescribed speed with fixed top and foreset slopes. The combined model of transport and progradation, is used to predict the transient trapping of saline water under an advancing shore-line across a range of realistic settings for shoreline velocity and aquifer hydraulic properties. For homogeneous aquifers, results indicate that the distance behind the shoreline, over which saline water can be detected, is controlled by the ratio of the shoreline prorogation rate to the aquifer velocity and the Peclet number. The presence of confining units probably had the greatest impact in sequestering onshore seawater behind an advancing shoreline. Further support for the validity of the proposed model is provided by fitting model predictions to data from two field sites (Mississippi River and Bengal Deltas); the results illustrate consistent agreement between predicted and observed locations of fossil seawater.