A computational study has been carried out to investigate smouldering ignition and propagation in polyurethane foam. The one-dimensional, transient, governing equations for smouldering combustion in a porous fuel are solved accounting for improved solid-phase chemical kinetics. Forward and opposed smouldering modes are examine and the model describes well both propagation modes. Specifically, the model predicts the reaction-front thermal and species structure, the onset of smouldering ignition, and the propagation rate. This is a signifficant step forward in smouldering combustion modelling, because unification of forward and oposed propagation modes had never been achieved before. This breakthrough is associated to the use of improved chemical kinetics obtained with a novel metodology to establish the reaction chemistry. The corresponding kinetic parameters for a reduced five step mechanisms of polyurethane foam smouldering kinetics are used. These kinetic mechanisms are then used to model one-dimensional smouldering combustion, numerically solving for the solid-phase and gas-phase conservation equations. A forced flow of oxidizer gas is considered and gravity neglected. The results from previously conducted microgravity experiments with flexible polyurethane foam are used for calibration and testing of the model predictive capabilities.