This thesis focuses on studying the interaction between floating objects and an air-water flow system driven by gravity. The system consists of an inclined channel in which a gravity driven two phase flow carries a series of floating solid objects downstream. Numerical simulations of such a system requires the solution of not only the basic Navier-Stokes equation but also dynamic interaction between the solid body and the two-phase flow. In particular, this requires embedding of dynamic mesh within the two-phase flow. A computational fluid dynamics solver, ANSYS fluent, is used to solve this problem. Also, the individual components for these simulations are already available in the solver, few examples exist in which all are combined. A series of simulations are performed by varying the key parameters, including density of floating objects and mass flow rate at the inlet. The motion of the floating objects in those simulations are analyzed to determine the stability of the coupled flow-solid system. The simulations are successfully performed over a broad range of parametric values. The numerical framework developed in this study can potentially be used in applications, especially in assisting the design of similar gravity driven systems for transportation in manufacturing processes. In a small number of the simulations, two kinds of numerically instability are observed. One is characterized by a sudden vertical acceleration of the floating object due to a strong imbalance of the force acting on the body, which occurs when the mass flow of water is weak. The other is characterized by a sudden vertical movement of air-water interface, which occurs when two floating objects become too close together. These new types of numerical instability deserve future studies and clarifications. This study is performed only for a 2-D system. Extension of the numerical framework to a full 3-D setting is recommended as future work.