The construction of a tunnel or a pipeline or a new harbour generally requires the dredging of a channel or trench in a river or estuary. Depending on the geometry of the channel, various morphological problems may arise such as sedimentation and erosion of the channel bed, local erosion near the head of the tunnel elements placed in the channel and local instability of the side slopes of the channel. Especially of importance for the dient as weil as the contractor are the morphological changes of the channel bed, which are caused by a local change of the flow velocity and hence the sediment transport capacity resulting in sedimentation in the deceleration zone and erosion in the acceleration zone of the channel. As a result of serious sedimentation problems which did occur in some large tunnel trenches dredged in the years 1960 to 1970 in the Netherlands, the Dutch Office for Public Works (Rijkswaterstaat) has requested the Delft Hydraulics Laboratory to develop a mathematical model for sedimentation predictions. The purpose of such a model should be the estimation of the sedimentation in relation to the channel geometry. This study, which started in 1972 within the framework of the applied research programme of the Rijkswaterstaat, resulted in a two-dimensional vertical mathematical model for suspended sediment (SUTRENCH-model). In Chapters 2, 3, 4, 5, 6, and 7 of the present communications report a detailed description of the SUTRENCH-model is given. In chapter 8 the flow field in a channel oblique to the flow is described. In Chapter 9 the influence of the most important hydraulic parameters on the predicted sedimentation rates is shown. Finally, an extensive verification analysis concerning flume experiments and field studies is given (pipe line channel in the Western Scheldt Estuary, the Netherlands; tunnel trench near Rotterdam; navigation channel near Korea). Futural developments will be focussed on quasi-three dimensional modelling of the suspended sediment transport to deal with converging, diverging and reversing flows.