This paper describes the development and validation of a comprehensive numerical model enabling the simulation of reinforced concrete beams at serviceability conditions using a discrete crack approach. The highly non-linear behaviour introduced by the different material models and the multiple cracks localising and propagating within the member pose a challenging task to classic iterative solvers, which often fail to converge. This limitation is solved with a non-iterative solution-finding algorithm, in which a total approach is used to overcome critical bifurcation points. The finite element model is validated using experimental data concerning lightweight aggregate concrete beams under flexural loading. The model is shown to properly simulate both overall and particular features of the structural response, including curvature, crack openings and crack patterns. The model is then applied to carry out a small parametric study on the role of the longitudinal reinforcement ratio and crack widths in reinforced concrete beams.