In this paper, hypopycnal and hyperpycnal particulate currents that are formed at river outflows in the sea are studied. The main aim is the use of CFD methods, in order to investigate the plunging mechanism in the case of hyperpycnal currents. Two series of numerical experiments are conducted. The first series, aims to validate the numerical model by checking its ability in capturing the critical suspended sediment concentration for plunging. The second series, aims to investigate the dependence of the plunge depth from the initial flow conditions, in the case of hyperpycnal currents. From the analysis of the results, an empirical equation is derived which relates the plunge depth with the initial conditions. It is also found that secondary hyperpycnal currents, can be generated indirectly, from hypopycnal currents, due to descending sediment fingers. The model predictions, in the present paper are in agreement with previous investigations.