A standard large-scale ice-sheet model is extended by (i) adding ice stream-shelf flow using a combined set of scaled equations for sheet and shelf flow, and (ii) coupling with a deforming sediment model that predicts bulk sediment thickness. The combination of sheet and shelf flow equations is heuristic, but allows horizontal shear and longitudinal stretching without a priori assumptions about the flow regime, and a freely migrating grounding line. The sediment model includes bulk transport under ice assuming a weakly non-linear till rheology, and generation of till by glacial erosion. The combined model explicitly simulates off-shore sediment strata, taking one step towards the goal of direct comparisons with Cenozoic glacimarine sediments on Antarctic continental shelves. Preliminary 1-D flowline simulations are described on a linearly sloping domain, with simple prescribed spatial and temporal variations of surface ice mass balance. Each simulation is run for 10 million years, and the various patterns of offshore sediment strata built up over the course of each run are examined. A wide variety of sediment patterns is produced depending on uncertain model parameters, including unforced irregular oscillations in the absence of external forcing variations. The results are not conclusive, but illustrate the variety of possible interactions that may play a role as more definitive 3-D models become available to link Cenozoic climate variations with the Antarctic sediment record.