We extend the class of simple offshore models that describe large-scale bed evolution in shallow shelf seas. In such seas, shallow water flow interacts with the seabed through bed load and suspended load transport. For arbitrary topographies of small amplitude we derive general bed evolution equations. The initial topographic impulse response (initial sedimentation and erosion patterns around an isolated feature on a flat seabed) provides analytical expressions that provide insight into the inherent instability of the flat seabed, the Coriolis-induced preference for cyclonically oriented features, and bed load transport being a limiting case of suspended load transport. The general evolution equation can be used to describe sandbank formation, known as the result of self-organization. Examples of human intervention at the seabed include applications to a dredged channel and an offshore sandpit. An outlook toward future research is also presented.