A computational Eulerian–Lagrangian model (ORSA2D_WT) is used for modelling the movement of floating rigid bodies on the water surface. The two-dimensional transport is computed with a dynamic approach, modifying existing formulations for the transport of bodies within fluid flows for the case of floating bodies, by adopting suitable added mass, drag and side coefficients. An original formulation for planar rotation is proposed, which includes the effect of the hydrodynamic torque and a resistance term, named added inertia, based on the difference between the angular velocity of the flow and that of the body. The value of the added inertia coefficient is calibrated against experiments made on purpose, involving the transport of a cylinder in a flume with two side obstacles. The calibrated code is applied to a slightly larger set of experiments for its preliminary evaluation. The outcome of the simulations shows that the streamwise and transversal displacements are well modelled, while some inaccuracies arise when considering the cylinder orientation. The effects of the initial conditions on the cylinders' trajectory and rotation are discussed, showing their influence on the evolution of the rotation angles.