A new smoothed particle hydrodynamics (SPH) scheme that models floating debris in shallow water tsunami flows is presented. The scheme is developed for debris-laden tsunami flows, one of the most deadly natural disasters, causing enormous destruction and loss of life. The debris transported by the violent surge has a significant role in destroying the inland structures. This thesis investigates the debris behaviour in shallow water flows, such as tsunami, to mitigate future flooding events. SPH is a meshless Lagrangian discretisation scheme whose major advantage is the absence of a mesh making the method ideal for highly non-linear flows with mixing of fluid and debris components which change with time. The 2-D shallow water equation (SWE) flow model is formulated as Euler-Lagrange equations for kinetic and potential energy providing mass and momentum/force conservation requiring solution by the iterative Newton method. A new SPH boundary treatment is presented extending the wall boundary conditions proposed by Adami et al. (2012) to depth-integrated shallow flows and is capable of imposing no-slip or free-slip conditions on general-shape solid walls. Open boundary conditions for SWE-SPH can impose inflow and outflow problems, explicitly intended for tsunami wave generation in this work. The implementation required major changes to open-source SPH solver DualSPHysics. The SPH scheme has been implemented to run on multi-core central processing unit (CPU) accelerated using OpenMP showing speed-ups of nearly six times on an 8-core processor compared to a single-threaded optimised code. The hydrodynamics code is extensively validated for a range of test cases including a dry-bed dam-break flow, a dry-bed dam break impacting and flowing around a static structure, steady flow over a bump using inflow-outflow boundaries, and comparison with experimental data for the Okushiri tsunami. A new formulation to include floating debris is proposed that captures two-way debris-fluid coupling. The hydrodynamic force acting on the debris is formulated in a three-dimensional (3-D) approach such that the debris can move in the vertical direction within the water column. The model can predict debris-debris, debris-bed and debris-wall interaction. The new SWE-SPH debris model is validated using a range of test benchmark cases including a floating debris in a hydrostatic tank with sloping bed, debris moving in uniform flow down a sloping channel, debris hit by a dam break surge and debris flow along a channel with side baffles comparing with experimental data. The SWE-SPH-debris model is applied in the Okushiri tsunami case where tens of individual debris are distributed throughout the domain near the shoreline. The results highlight the different behaviour observed for debris with density greater than or less than water.