The analytical tools necessary for the implementation of inelastic methods for bridges are presented. The chapter starts with available models for the bridge deck and their role in seismic assessment, addressing not only elastic modelling of the deck but also far less explored issues like the verification of deck deformation demands in cases that inelastic behaviour of the deck is unavoidable. Then the topic of modelling bearings and shear keys is presented, which is of paramount importance in the case of bridges, logically followed by the related issue of seismic isolation and energy dissipation devices; modelling of all commonly used isolation and dissipation devices is discussed and practical guidance is provided. The next section is devoted to inelastic modelling of different types of bridge piers, which are the bridge components wherein seismic energy dissipation takes place in non-isolated structures. All types of inelastic models for members, with emphasis on reinforced concrete columns, are presented in a rather detailed way, including both lumped plasticity and distributed plasticity models. Several examples of application of the previously mentioned models to bridges of varying complexity are provided and critically discussed. The last two sections of the chapter deal with modelling of the foundation of bridges and its interaction with the ground. Simple and more sophisticated models for abutments and (surface and deep) foundation members are provided, followed by models for the surrounding ground, with emphasis on the embankments that often play a crucial role in the seismic response of bridges, in particular short ones. Soil-structure interaction modelling of bridges is presented in both its commonly used forms, i.e. linear, as well as nonlinear soil-foundation-bridge interaction analysis in the time domain. These last sections of the chapter also include a brief overview of the characteristics of seismic ground motion which is used as input for the analysis.