Non-Newtonian fluids are of great scientific interest due to their range of physical properties, which arise from the characteristic shear stress-shear rate relation for each fluid. The applications of non-Newtonian fluids are widespread and occur in many industrial (e.g. lubricants, suspensions, paints, etc.) and environmental (e.g. mud, ice, blood, etc.) problems, often involving multiple fluids. In this study, the novel technique of Incompressible Smoothed Particle Hydrodynamics (ISPH) with shifting (Lind et al., J. Comput. Phys., 231(4):1499-1523, 2012), is extended beyond the state-of-the-art to model non-Newtonian and multi-phase flows. The method is used to investigate important problems of both environmental and industrial interest.The proposed methodology is based on a recent ISPH algorithm with shifting with the introduction of an appropriate stress formulation. The new method is validated both for Newtonian and non-Newtonian fluids, in closed-channel and free-surface flows. Applications in complex moulding flows are conducted and compared to previously published results. Validation includes comparison with other computational techniques such as weakly compressible SPH (WCSPH) and the Control Volume Finite Element method. Importantly, the proposed method offers improved pressure results over state-of-the-art WCSPH methods, while retaining accurate prediction of the flow patterns.Having validated the single-phase non-Newtonian ISPH algorithm, this develops a new extension to multi-phase flows. The method is applied to both Newtonian/Newtonian and Newtonian/non-Newtonian problems. Validations against a novel semi-analytical solution of a two-phase Poiseuille Newtonian/non-Newtonian flow, the Rayleigh-Taylor instability, and a submarine landslide are considered. It is shown that the proposed method can offer improvements in the description of interfaces and in the prediction of the flow fields of demanding multi-phase flows with both environmental and industrial application.Finally, the Lituya Bay landslide and tsunami is examined. The problem is approached initially on the real length-scales and compared with state-of-the-art computational techniques. Moreover, a detailed investigation is carried out aiming at the full reproduction of the experimental findings. With the introduction of a k-ε turbulence model, a simple saturation model and correct experimental initial conditions, significant improvements over the state-of-the-art are shown, managing an accurate representation of both the landslide as well as the wave run-up. The computational method proposed in this thesis is an entirely novel ISPH algorithm capable of modelling highly deforming non-Newtonian and multi-phase flows, and in many cases shows improved accuracy and experimental agreement compared with the current state-of-the-art WCSPH and ISPH methodologies. The variety of problems examined in this work show that the proposed method is robust and can be applied to a wide range of applications with potentially high societal and economical impact.