Since turbulent diffusion is a stochastic phenomenon, it is hard to describe dispersion in a river deterministic formula, and no exact theory can be formulated. Simulation techniques are more promising in this respect. This paper described simulations of horizontal dispersion of tracer material from a finite and continuous source. A stochastic model by which the horizontal dispersion of a number of particles can be simulated was developed. The model accounts for the increased dispersion caused by horizontal shear. The input data required for the model were determined from field measurements carried out at four positions in the Lule River, after which the stochastic model was applied to an 8 km long reach of the river. It was found that Fickian Law of dispersion was not applicable since the dispersion coefficients grew still faster but were linear