Numerical simulation methodologies have become a major approach for solving hydrodynamics problems over the past few decades. Due to their flexibility and adaptability, these methods can be employed in various subjects of engineering and science. These simulations are capable of providing the required knowledge to interpret the natural phenomena and as well can be an alternative means to study the theories and experiments. Numerical modeling of fluid flow can be categorized into two major approaches, mesh-based methods and mesh-free methods. Mesh-based methods used to be the dominant methods through the decades but their lack of success in the precise simulation of flow problems with considerable deformation and fragmentation resulted in the development of mesh-free methods. Mesh-free methods use a set of discrete particles and the field variables are assigned to each particle separately. As a result, the movement of the particles is a direct expression of the movement of the real physical system. Mesh-free methods have proven to be a robust tool in numerical simulation and yet to their fully extended application in the hydrodynamics simulations. In this thesis the Weakly-Compressible Moving Particle Semi-implicit (WC-MPS) method is described and demonstrated for the simulation of the dam-break case with a high viscous fluid on different bed slopes. During this study, at first the WC-MPS was applied to a horizontal case and the model was later modified to numerically study the effect of bed slopes on the dam-break case. Furthermore, the process of gate removal at the initial stage of the dam-break case and its influence on the flow current development were investigated. This investigation demonstrated that the process of gate removal can have a considerable effect on the formation and development of flow current in a dam-break case. At last, the capability of WC-MPS model to simulate open channel flow problems is confirmed through a comprehensive comparison with analytical and experimental studies. The simulations in this thesis demonstrate that WC-MPS can be used as a robust tool in simulation of fluid flow especially in problems with large pressure gradients and fast varying fluid levels. To maintain stability, a small time step is needed that unfortunately leads to considerable calculation time. To obtain an accurate simulation many particles should be employed, therefore the application of this method is restricted to local and short phenomena. Although WC-MPS is a relatively new technique in the field of computational fluid dynamics but it can be used in situations where many other methods fail, therefore its future looks promising.