A numerical model presented here develops a three-dimensional image of alluvial media on an elementary scale significant for groundwater flow modelling. The model was tested on the alluvial plain of the Rhône River (France), on a scale of several kilometres and, from geomorphological observations and dating, reproduced the construction of this alluvial plain from ≈15 000 years BP to the present. The history of the alluvial plain during the Late Glacial and Holocene periods is summarized. Through most of this time, the River Rhône has maintained a braided pattern, with the exception of two incising phases with a meander pattern. The model does not use any physically based equations or water representation. The main processes governing the construction of the plain are modelled by simple rules chosen according to geometrical or empirical laws taken from the literature or as modelling assumptions. Using multi-agent concepts of distribution and interaction of elementary entities, these sedimentary rules are applied to ‘sediment’ entities or to conceptual ‘erosion’ entities that simulate local deposition and erosion of sediments. The sedimentation model reproduces the various climatic periods during which the sediments were deposited by simulating genetic periods and associated modelled processes. For each period, the model was constrained by quantitative field data such as altitude of ancient channels and deposits or thickness of sediments. The general geometry of the alluvial deposits was satisfactorily reproduced. During the simulation, characteristic large-scale features emerge despite the use of local rules. The model results are discussed with reference to other approaches, such as geostatistical or Boolean models, and the applicability of the model to other less documented alluvial plains is outlined.