Yes / Natural earth-bounded channel flows usually subject to various sidewall turbulences, i.e. in the form of secondary currents, due to non-constant channel shapes at different sections. This paper investigates an improved Shiono-Knight model (SKM) by combining it with a Multi-Zonal (MZ) method (proposed by Pu, 2019) to represent lateral flow turbulence and secondary currents in different shapes of open channel, i.e. rectangular and trapezoidal. By applying the proposed analytical model to both rectangular and trapezoidal channel flows, we have inspected different streamwise velocity characteristics across transverse direction generated by their sidewalls in order to provide crucial fundamental understanding to real-world natural flow system. The proposed model has also been validated via various experimental data conducted in national UK Flood Channel Facility (UK-FCF). It has been observed that the trapezoidal channel has created a larger sidewall zone where secondary current can affect flow velocity; however, the intensity of the secondary flow in trapezoidal channel has been found lesser than that of the rectangular channel. By improving the modelling of natural flow at sidewall, the studied approach could be adapted into different existing analytical models to improve their accuracy.