AbstractIn the present paper, a finite element model is developed based on a semi-discrete Streamline Upwind Petrov-Galerkin method to solve the fully-coupled two-dimensional shallow water and contaminant transport equations on a non-flat bed. The algorithm is applied on fixed computational meshes. Linear triangular elements are used to decompose the computational domain and a second-order backward differentiation implicit method is used for the time integration. The resulting nonlinear system is solved using a Newton-type method where the linear system is solved at each step using the Generalized Minimal Residual method. In order to examine the accuracy and robustness of the present scheme, numerical results are verified by different test cases.