Assessment of existing buildings making use of numerical simulation methods, even under the hypothesis of full knowledge of current conditions and materials, it is not an easy and straightforward task due to the limitations and complexities of such analysis tools. In this chapter, a discussion of different approaches for the simulation of structural response is introduced and applied to two of the most common building typologies: masonry structures and reinforced concrete frames. Following a brief introduction of the problematic, an overview of different modelling possibilities for masonry structures is presented. Afterwards, choices made during numerical modelling are discussed, based mainly on the finite element method. Moreover, the problematic of different modelling techniques is addressed, where some paths and best practices are suggested. The last section is devoted to the response simulation of reinforced concrete structures. Efficient frame elements and sectional models, which allow capturing an extended range of elastic and inelastic response, are analysed first. Strut-and-tie modelling is then recalled as a powerful analysis tool, and its application to the assessment of old buildings is studied.