Natural debris floods travel in straight and meandering courses. The flow behaviour greatly depends on the volume fractions of solid and fluid, as well as on their dynamic interactions with the channel geometry. For the quasi three-dimensional simulations of flow dynamics and mass transport of these floods through meandering and straight channels, we employ a two-phase debris flow model to carry out simulations for debris floods within straight and sine-generated meandering channels of different amplitudes. The results for different sinuous meandering paths are compared with that in the straight one in terms of phase velocity, downslope advection and dispersion, depths of the maxima, deposition of mass, position of front and rear parts of the solid and fluid phases, and also the flow dynamics out of the conduits. The results reveal the slowing of the flow and increase of momentary deposition of the mixture mass in the vicinity of the bends along with the increasing sinuosity. The numerical experiments are useful to better understand the dynamics of debris floods down meandering channels as seen in the natural paths of the rivers as well as already existing channels like episodic rivers in hilly regions. The results can be extended to propose some appropriate mitigation strategies.