Understanding the relationship between sedimentation and tectonics is critical to the analysis of stratigraphic evolution in foreland basins. Previous models of foreland basins have explained stratal development, but were done generally under the assumption that steady allogenic forcing produces a steady stratigraphic response. They did not consider autogenic shoreline behaviour during the development of the subsidence pattern characteristic of foreland basins. We present a mathematical model and flume experiments that explore how subsidence and sediment-supply rates control the shoreline trajectory and the stratal patterns that fill foreland basins. Through these models, we found differing autogenic responses in the rate and direction of shoreline migration, and these generated three distinct styles of stratal architecture, despite the constant external forcing (i.e. constant sediment discharge and basin substrate tilting). The first response was ‘autoretreat’, where shoreline migration switched from initial progradation to retrogradation. The second response was progradation followed by constant aggradation of the shoreline. The third response was maintained progradation with a markedly accelerating rate. We termed this latter newly observed autogenic behaviour ‘shoreline autoacceleration’. These three modes of shoreline behaviour and their accompanying stratal architecture provide a basic framework for the relationship between sedimentation and tectonic activity in foreland basins under the simplified conditions presented here.