||Different from the majority of current numerical approaches, the Kinetic Flux Vector Splitting (KFVS) scheme, based on kinetic theory described by the collisionless Boltzmann equation, is formulated, implemented and applied in this thesis. The scheme is explicit and first order in both space and time. Its stability criteria is required by Courant number (Cr)≤ 1. From taking zeroth and first moments of the collisionless Boltzmann equation, the mass and momentum conservation laws for open channel flows are obtained. This consistency allows us to construct the 1-D and 2-D KFVS schemes to solve typical open channel problems from a mesoscopic point of view. In the development of the mathematical procedure of the KFVS scheme, some moments of the equilibrium distribution function in the particle velocity space establish the links between mesoscopic and macroscopic quantities. It is found that it is straightforward to extend this scheme from 1-D case to 2-D case. Through the performance in a range of typical 1-D and 2-D open channel test cases, it is shown that the KFVS scheme has good accuracy, is easy for programming, and still maintains a high efficiency. It will be promising to investigate the potential capability of this scheme in being applied for problems with practical background.