Computer-based numerical simulation has become a significant and very popular approach for solving engineering problems in the past few decades. It provides a safe and efficient tool to engineering investigations. It can even provide the knowledge that cannot be obtained directly through other methods. In other words, numerical simulation provides the assistance to interpret the theoretical phenomena and offers an alternative way to insightfully study the theories or experiments. In hydrodynamics simulations, the tradition mesh-based methods have been the dominant methods for decades, but they will fail in the simulation of free surface flow problems due to the large deformation and fragmentation, and they suffer from some problems whose objects are a set of discrete physical particles (rather than a continuum). On the contrary, mesh-less particle methods (MPMs), or mesh-free particle methods, whose domain discretization is based on a finite number of discrete particles. The state and movement of the problem system is represented by a set of discrete particles in MPMs. As in computational fluid dynamics (CFD) problems, the field variables, such as location, velocity, pressure, force and other variables (e.g. mass, momentum, energy) are included into each particle. Therefore, the movement of the real physical system is directly reflected by the movement of the particles. In the past decades, the MPMs have been proved as a robust tool in numerical simulations, it is expected that the mesh-less method will further thrive the numerical studies in fluid mechanics. This study reposes upon the weakly-compressible moving particle semi-implicit (WCMPS) method modified and improved by Shakibaeinia and Jin (2010) and aims at modifying the WC-MPS model and applying it to free surface flow problems. During this study, the complete theory of the proposed WC-MPS model was introduced. The model was later modified to numerically study several open channel flow problems with open boundaries. Furthermore, non-Newtonian fluid flows were studied and the specified WCMPS method for simulating non-Newtonian flows was proposed. Through the current study, the capability of the proposed model to simulate open channel flow problems was confirmed. And the proposed model successfully reproduced the important flow features for the real open channel flow problems with open boundaries. Further modification and application of the proposed model to simulate non-Newtonian fluid flows had been validated through experimental studies and the model reproduced the crucial non-Newtonian flow features. Comparison with experimental tests showed that WC-MPS is capable to simulate free surface flows of non-Newtonian fluid flows.