This chapter describes the mechanical methods for seismic vulnerability assessment of buildings. It aims at establishing the theoretical foundation of pushover analysis or nonlinear static analysis and fragility curves, along with the contributions and limits associated with these two aspects of seismic engineering. It shows the use of "classic" nonlinear static analysis compared to other methods of analysis but also the critical points, especially concerning the use of superior modes and lateral force invariability. The chapter presents the latest developed methods in an attempt to solve these two difficulties, leading to new nonlinear static methods known as "multimodal" and "adaptive". The determination of the performance point (PP) has been presented through different methods. Concerning fragility curves, the chapter describes the different approaches to derive capacity curves: semi-empirical models, empirical models based on observations, models based on expert judgment, mechanical models and hybrid models, along with the recent studies.