This paper investigates 1D-modelling of non-uniform flows in compound channels. The issue is how to accurately predict both flow depth and mean velocity in the floodplain. A new model, called Independent Sub-sections Method (ISM), is presented here. Unlike classical 1D models that solve a dynamic equation on the total cross-section, the ISM estimates the water surface profile within each sub-section. This enables the water level and the sub-section mean velocities to be simultaneously calculated, without priority to any variable. In opposition to the DCM, corrected DCM or the EDM, the ISM assumes independent evolution of the discharge in each sub-section of the compound channel. Indeed, this method does not assume equal head loss gradients in all sub-sections, and it does not impose the downstream discharge distribution. The ISM consists in a set of three coupled 1D momentum equations (written within main channel, left-hand and right-hand floodplains) and a mass conservation equation on the total cross-section. Mass and momentum exchanges at the interfaces between sub-sections are explicitly accounted for. This method is validated against experimental data for: developing flows in straight compound channel, flows in skewed compound channel, in a symmetric converging or diverging compound channel, and in an asymmetrical compound channel with an abrupt floodplain contraction. For the 46 runs, the ISM predicts flow depth and mean velocity in the floodplain with a maximum relative error of 8% and 19% respectively. The ISM also appears to be a useful theoretical tool to improve our understanding of physical processes governing compound channel flows.