**Abstract**

This chapter consists of four sub-chapters the first of them is the introduction. The second sub-chapter discusses the suitability of the explicit and implicit methods for seismic analysis of buildings exposed to a substantially nonlinear response. Taking into account a duration typical for earthquakes from several seconds to about twenty seconds, it seems that the implicit method is more suitable. Because of the shape of accelerograms, it is needed to use quite short time steps. Both methods were compared for a heavily nonlinear response, typical for seismicity. The third subchapter discusses the analysis of the time-dependent behavior of concrete using nonlinear timedependent material models during fast dynamic actions. Huge plastic yielding or damage of the material is reached. The fourth sub-chapter discusses sources of dynamical damping that are needed in earthquake analysis. This subchapter aims to take into account the influence of different kinds of damping in the dynamic analysis of structures. More advanced analysis taking into account the various sources of damping, i.e., material viscosity, plasticity/damage, and friction in connections and supports is strongly recommended in the earthquake analysis.

**Keywords:** earthquakes, seismicity, dynamics, transient, implicit, explicit, finite element method, plasticity, damage, viscosity, damping
