Rivers polluted by plastics have become sites where mixtures of microplastics and sediment particles are transported by the river current and deposited in the riverbed. A hydromorphodynamic numerical model was developed using Delft3D (software specialized in simulating natural water systems), to simulate the sedimentation, erosion, resuspension and transport of microplastics together with sediment particles, introducing an innovative model with an active riverbed. The model was used to understand the distribution patterns, morphological changes and load balances of plastic debris in a river. The study case is an artificial braided river with a non-buoyant suspended microplastic load. The results simulate a sediment bed that acts as a source of microplastic storage near the point of release. The high deposition of microplastics increases the capacity of the river flow to erode the banks and channels, resulting in deeper channels and larger river bars. The highest amounts of microplastics were deposited in the inner channel banks, and the highly suspended microplastic load is transported in the main channel thalweg. The model can be used as a more accurate method to predict the dynamics of microplastic fluxes in rivers, providing better tools to understand how much plastic enters the ocean from the river environment. This article is part of the Theo Murphy meeting issue 'Sedimentology of plastics: state of the art and future directions'.