The Finite Element and Boundary Element Methods are both well established numerical techniques for analysing a wide range of engineering problems. In the present thesis these numerical techniques are used for obtaining a more realistic picture of various characteristics of concrete gravity dams. The present work addresses the behaviour of gravity dams under static loading, and the developed analysis procedure/computer package can cater for a wide range of dam characteristics including: the three-dimensional behaviour of a gravity dam-foundation-abutments system; the non-linear behaviour of a dam and foundation materials; the sequential construction of a dam and impounding of the reservoir loading on the structure; the effect on stresses of interfaces and joints existing between a dam and its foundation, and in the body of a dam itself; the action of pore water pressure within the foundation, at the dam-foundation interface, and in the body of a gravity dam; etc. Using the purpose written computer package which can cater (in an efficient and accurate way) for the influence of all such factors, mathematical programming methods are, then, used to produce a powerful tool for the shape optimisation of gravity dams leading to safe, functional and economical solutions to the problem. In the course of developing the computer program, much care has been exercised as regards the appropriate selection of the finite element types, mesh configurations and mesh densities, in order to reflect (in an efficient fashion) the variation of stress gradients in the body of a gravity dam. In order to reduce high costs associated with a full three-dimensional analysis, a rather efficient method is developed which enables one to carry out equivalent twodimensional computer runs which will effectively simulate the actual three-dimensional behaviour of gravity dams in, for example, narrow valleys. The proposed approach reduces the dimensionality of an actual problem by one, thus, eliminating the main disadvantage of the finite element method in terms of high solution costs for threedimensional problems. As a result, the proposed method makes the solution procedure highly cost effective. By coupling the finite element-boundary element (FEBE) techniques, which can cater for the material non-linearities in the appropriate regions of the foundation, an attempt is made to by-pass the individual disadvantages of both these numerical techniques. It has, then, been possible to exploit the advantages of reducing the dimensionality of the foundation region by one using the boundary element technique, and, hence, come up with significant savings in terms of computer running times. Anisotropic tangent constitutive models for plain concrete under a general state of biaxial static monotonic loading for, both, plane-stress and plane-strain states of stresses are proposed which are simple in nature, and use data readily available from uniaxial tests. These models have been implemented into the computer program which is, then, used to investigate the influence of the step-by-step construction of the dam and the sequential impoundment of the reservoir loading on the state of stresses. The non-linear program is also used to analyse various characteristics of Bratsk concrete gravity darn (in Russia). The correlations between the numerical results and extensive field measurements on this darn, have been found to be encouraging. Isoparametric quadratic interface finite elements for analysing the darnfoundation interaction problem have also been developed. These elements have zero thickness and are based on an extension of the linear interface elements reported by others. The numerical problems of ill-conditioning (usually associated with zero thickness elements) are critically investigated using test examples, and have been found to be due to inadequate finite element mesh design. Non-linear elastic tangent constitutive models for simulating the shear stress-relative displacement behaviour of interfaces have also been developed, and are used to analyse the effects of including interface elements at the dam-foundation region of contact. It is shown that the inclusion of interface elements in the numerical analyses of the dam-foundation system leads to rather significant changes in the magnitudes of the critical tensile stresses acting at the heel of the dam, which have previously been evaluated (by others) using a rigid dam-foundation interconnection scheme. Effects of pore water pressure, acting as a body force throughout the foundation, the dam-foundation interface and the body of a gravity dam, are also critically studied, with the pore pressure values predicted by seepage analysis. Using an extensive set of numerical studies, a number of previously unresolved issues as regards the influence of pore pressures on the state of stresses are clarified. The effect of drainage on the state of stresses within the body of a dam is investigated, and an insight is also given into the effect of the uplift acting at the lift lines between successive layers of Roller Compacted Concrete (ReC) dams. A shape optimisation procedure for gravity dams based on the penalty function method and a sequential unconstrained minimisation technique is also developed. A number of shape optimisations of idealised gravity dams are carried out in order to compare the numerical results with previously available analytical solutions. The present work also caters for the effects of foundation elasticity and uplift on the optimal shape of a gravity dam. A numerical example is provided covering the shape optimisation of a hollow gravity dam. Finally, the shape optimisation of an actual dam (i.e. Tvishi gravity dam in Georgia) using the presently proposed procedures is carried out with the fmal results compared with those available from the project design team. Wherever possible. numerical outputs have been checked against available small or full scale test data or previously reported closed form solutions. Throughout this thesis very encouraging correlations between the present predictions and such experimental and theoretical data have been obtained.