A dynamic mathematical model has been constructed for the computer simulation of sedimentation in free meandering streams. The system is defined in terms of form and process, and component mathematical models (with mainly deterministic, but also probabilistic, characteristics) are formulated for the prediction of the following aspects of the system for a given physical situation and a single time increment; (l) The characteristics of the plan form of free meanders; (2) The movement of meanders in plan, and definition of cross sections across the meander in which erosion and deposition are considered in detail; (3) The hydraulic properties of the channel and the erosional and depositional activity within the channel as defined in specific cross sections; (4) Whether neck or chute cut off will occur; (5) A relative measure of the discharge during seasonal high water periods, which s is used in (3) and (4); (5) Aggradation. The limitations, qualifications and validity of the component mathematical models are discussed during their development, as is the input required. The overall model has been translated into a FORTRAN IV computer program and a set of experiments with selected input parameters has been performed. The results and their implications are fully documented and compared qualitatively with recent and ancient fluviatile sedimentation. The shape of simulated pointbar sediments, as controlled by channel migration over floodplains of variable sediment type, agrees broadly with the natural situation. Sheet deposits cannot be simulated because large-scale meander-belt movements are not accounted for; this also inhibits generation of thick sequences of alluvial sediments. When channel, migration is combined with a constant aggradation rate the model predicts a general slope (relative to the land surface) of facies boundaries and scoured basal surfaces upward in the direction of channel movement. If aggradation sufficiently increases the thickness of fine grained overbank material, there is a channel stabilisation effect. Epsilon cross-stratification, which represents the shape of a pointbar surface before falling-stage deposition (lateral and vertical), may be picked out in the simulated sediments. The epsilon unit thickness is that measured from bankfull stage down to the lowest channel position existing prior to deposition. The model records the characteristic fining upwards of grain sizes in the pointbar, and the systematic distribution of sedimentary structures. Channel migration combined with seasonal scouring and filling across the channel produces a characteristic relief in the basal scoured surfaces and the grain size and sedimentary structure boundaries. A related lensing and inter- fingering of grain size and sedimentary structure facies may also be present. The model also records large-scale lateral changes in grain size and sedimentary structure associated with changes in the shape of developing meanders. It is shown that a complete sequence of pointbar sediments capped by overbank sediments would rarely be preserved in the moving-phase situation. Such preservation only becomes likely when an aggrading section lies out of range of an eroding channel for a considerably longer time span than it takes a meander to move one half-wavelength downvalley. Deep channel-scours have a higher preservation potential than contemporary shallower ones. Where appropriate field data exist the model can be used in the more accurate recognition of ancient fluviatile sediments. Inferences may be made about the erosion-deposition processes operating in the ancient channel system, and the geometry and hydraulics of the system can be alluded to. A representative application of the model to the quantitative interpretation of an ancient pointbar deposit is illustrated. There is reasonable agreement between the natural and the simulated deposits, and a broad quantitative picture of the palace environment of sedimentation is obtained.