Mining is a booming industry and it indirectly involves everyone living in modern society. Tailings, the primary solid waste generated as the side effect of extracting valuable minerals, often require vast facilities to store the large quantity of waste. Failure of tailings storage facilities often causes significant damage both environmentally and economically, and frequently results in fatalities. Nowadays numerical simulation of tailings flows resulting from potential failures has become widespread in practice to assist the design of tailings storage facilities. In this thesis, tailings runout simulations are attempted using a numerical method suitable for large deformation analysis (Material Points Method) employing an advanced rheological model. This study aims to simulate the runout of tailings dam breach incident such as Merriespruit in South Africa using realistic geotechnical properties and producing results that fulfill the expectations from both geo-mechanical and hydrodynamical requirements.