The aim of this thesis is to provide an investigation toward a rigorous derivation of a stable and consistent numerical method based on the established Smoothed Particle Hydrodynamics method. The method should be suitable for modelling the large deformation transient response of fluids and solids, the interests of the Crashworthiness, Impact and Structural Mechanics group (CISM) at Cranfield University. A literature review of the current state of the art of the SPH method finds that the conventional SPH equations are not derived in a rigorous way, often the equations are manipulated into a mathematically equivalent form in order to preserve conservation of linear momentum, which often leads to different results; the reasons for this are unknown and it is not fully understood how each particular form of the discrete equations effects the solution in terms of stability, accuracy and convergence. This leads to specific objectives being defined which underpin the overall aim of the thesis. The first objective is to develop an understanding of the SPH method and the implementation used at Cranfield University, this is done through a capability study which demonstrates the coupled SPH-FE method and a number of relevant improvements to the MCM code including the addition of a turbulence model and the modification of the SPH contact algorithm to model lateral forces between materials. This is demonstrated through the implementation of a friction model, which suggests that the contact algorithm is suitable for resolving lateral forces based on the relative velocity between materials, with the potential for coupling with a structural FE model ... [cont.].