Abstarct: The finite deformation theories have been widely used in conventional deformation analysis of geomaterials. The finite element method (FEM) is often used as a numerical method in computational modelling. However, dealing with the large deformation and failure is generally a difficult task for FEM since this method is suffered from tough grid distortions. The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational modelling and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post-failure of geomaterials. This method is a kind of particle method baxsed on the mesh-free Lagrangian scheme, and is one of the promising numerical methods in the field of geotechnical engineering. Therefore, the method can represent the entire deformation process of soil from the small strain region to the large deformation region. In this thesis, first, basic theory and formulation of the SPH method baxsed on fluid mechanics are summarized. Then formulations of solid mechanic that we used to develop of hydrodynamics code are discussed. This code includes an elasto–plastic constitutive model for soil and a Navier–Stokes equation baxsed model for water. Also, the Drucker–Prager model is implemented into the SPH code to describe elastic–plastic soil behavior. All parameters have their physical meaning in soil mechanics and can be obtained from conventional soil mechanics experiments directly. Finally, two numerical examples analysis of cohesive soil slope in stability and an example for collapse of a granular slope are shown to check the capability of developed SPH code for modelling large deformation of slope failure. Logical critical slip surfaces are determined from a contour plot of accumulated plastic strain. baxsed on the output contour plot of some variable like deformation, velocity, stress and plastic strain, the effectiveness of the code of SPH is discussed from the point of view of geotechnical engineering. Good agreement with the results of simulations and theoretical solutions is obtained. So, this developed solid SPH code can simulate large deformation and post-failure of soil with high accuracy, and can thereby treat a wide range of applications in geotechnical problems.