Sediment routing simulation models are designed to reproduce the hydro-morphodynamic behaviour of natural rivers as completely as possible.Three- and two-dimensional models are accurate but time- consuming. Hence, they usually are not suitable for long-term simulations. Such purpose currently requires one- dimensional models, which ignore the lateral variations of the scour/deposition processes within the cross- section.This paper aims at including those effects for reliable predictions of lateral channel deformation.This is accomplished by solving in a coupled way the De Saint Venant-Exner equations. The resulting exchanged sedi- mentvolumes(scour/deposition)arethenpartitionedalongthecross-sectionbyusingatwo-dimensionalversion of the mass conservation laws (for both water and sediments), thus extending the one-dimensional model to a quasi-two-dimensionalmodel.Theproposedformulationistestedagainsttheresultsofafullythree-dimensional model in some idealized benchmark problems.Then, the influence of the quasi-two-dimensional reconstruction isevaluatedinsomeone-dimensionalproblems.Thedifferencesbetweenformulationscurrentlyusedinliterature and the proposed model become more clear as the role of the cross-sectional shape gains relevance.