A numerical model has been developed to simulate the input of radionuclides into the Mediterranean Sea through the Rhone River plume. The model is fully 3D. It solves the hydrodynamic equations, which include baroclinic terms and a turbulence model, together with the suspended sediment equations and radionuclide dispersion equations. The suspended sediment sub-model includes four particle classes, settling and deposition. The radionuclide equations include the exchanges of radionuclides between water, suspended sediments and bed sediments, described using a kinetic model. The effect of salinity changes upon uptake kinetics has also been included. Computed water circulation, salinity pattern, suspended sediment distribution and sedimentation rates are in agreement with observations in the area. The model has been applied to simulate the dispersion of 137Cs and $^{239,240}$Pu through the plume. Computed specific activities in water, suspended matter and bottom sediments are in agreement with the measured distributions. The model can also be applied to calculate distribution coefficients. Although some water circulation models for the Rhone River plume exist in current literature, this is the first time in which a detailed hydrodynamic and suspended sediment model has been applied to simulate the dispersion of radionuclides in the plume.