This paper focuses on numerical modelling of non-uniform flows in prismatic and non-prismatic compound channels. A new 1D computation methodology is presented which is called Independent Subsections Method (ISM). While conventional 1D models solve the momentum or energy equation on the overall cross-section area, the ISM treats the flow dynamics in the main channel and the floodplains separately. It solves an ordinary differential equations system which calculates the water level and mean velocity in the floodplains and the main channel, simultaneously. This method accounts explicitly for lateral mass exchanges, interfacial shear stress and associated momentum transfer between subsections. ISM simulations of water level and subsection velocities are in agreement with experimental data for four different geometries: straight compound channel; slightly narrowing floodplains; abrupt floodplain contraction; and skewed floodplain boundaries.