Cellular automata (CA) represent an interesting approach to the modelling of dynamical systems evolving on the basis of local interactions and internal transformations. The CA model, specially developed for simulating density currents, is described. The objective is to predict the formation and evolution of channels and the structure of deposits associated to the flow path. For simulation purposes, currents are represented as a dynamical system subdivided into elementary parts, whose state evolves as a consequence of local interactions and internal transformations within a spatial discrete domain. The model is developed for unsteady, two-dimensional, depth-averaged, particle-laden turbulent underflows driven by gravity, acting on density gradients created by non-uniform and non-cohesive sediment. CA is defined as a tessellation of finite-state automata (cells). The attributes of each cell (substates) describe physical characteristics. The natural phenomenon is decomposed into a number of elementary processes, with a particular composition that makes up the transition function of the CA. By applying this function to all the cells simultaneously, the evolution of the phenomenon can be simulated in terms of modification of the substates. The transition function includes the effects of water incorporation at the suspension–ambient fluid interface, a transport equation for the particle volume concentration, and a toppling rule for the deposited sediments. Simple and flexible, the obtained model constitutes a first step toward quantitative comprehension of the impact of external parameters on the turbidity current dynamics and on the organisation of the subsequent depositional sequences.