A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Master’s in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyA particle model for describing and predicting sediment transport in shallow water is developed with the use of random walk models by showing consistency between the Fokker-Plank equation and the Advection diffusion equations. In the model, erosion and deposition processes are developed probabilistically where by the erosion term is considered to be a constant and deposition term is taken as a function by relating sediment settling velocity and diffusion coefficient. The model was simulated by considering three environment tests. In each environment test, the simulations show the distribution of each particle at any given time t. They also show the particles that will finally remain in suspension state and the particles that will be deposited during the transport process following the deployment of 10 000 particles. It was established that there is uniform distribution of particles in test environment I and III and a linear dependence between the number of particles in different grid cell and the water depth in test environment II.