In the present thesis a three-dimensional finite element model for non-linear dynamic analysis of (1) seismic site and structure response and (2) soil-structure interaction with contact discontinuity is proposed and discussed. Accordingly, two numerical studies are presented, each consisting of a series of analyses of a coupled structure - foundation - soil system. In the first study a series of numerical examples are presented which include modelling of a reinforced concrete frame with a portion of the ground consisting of various horizontal layers resting on rigid bedrock. The influence of the ground layer configurations on the structure response due to seismic loads is investigated and discussed. In the second study the influence of various parameters governing the structure response, with emphasis on sliding and rocking of the structure, are investigated by assuming discontinuity in the soil - foundation interface. The spatial discretisation is performed by a combination of linear tetrahedral (ground) and hexahedral (structure) finite elements. The time integration is carried out by explicit integration using the leap-frog method. Total Lagrange formulation is adopted to account for large rotations and large displacements (geometrical non-linearity). To account for cracking and damage of the concrete, the frame structure is modelled by the microplane model (material non-linearity). Damage and cracking phenomena are modelled within the concept of smeared cracks. Plasticity model is used for the modelling the reinforcement and the ground adopting the Von Mises and Drucker-Prager yield criteria, respectively. The usual continuum assumption when treating the soil-foundation interface is replaced with a contact discontinuity approach in order to be able to capture foundation sliding and/or uplifting and rocking (contact non-linearity). Coulomb frictional model is adopted in the contact resolution. The proposed finite element code demonstrate the possibilities of advanced numerical approaches in simulation of complex engineering problems. Comparative analysis shows the importance of the local site conditions and influence of material non-linearity in seismic structural design. With the implemented microplane model, which is aimed to be used for fracture and damage analysis of concrete, it is possible do assess the sustained structural damage. Furthermore, for extreme scenarios with highly geometrically non-linear behaviour, as sliding and rocking, the proposed model of foundation - soil interface is more adequate than usual continuum approach with spring - dashpot elements and at the same time maintains a reasonable computational efficiency.F