**1. Introduction**

In the last decades, a big development in the field of nonlinear and time-dependent material models, including those that are suitable for seismic analysis, were achieved. But to take advantage of these developments, the use of spectral analysis must be abandoned and a method of direct integration of the equation of motion must be used (also called the transient or time history analysis). Several aspects of this area, including the comparison of the explicit and implicit method in seismic analysis [1, 2], suitable material models, and sources of dynamic damping are discussed in this chapter. Subchapter 2 deal with several aspects of the transient dynamic approach in seismic analysis. Subchapter 3 compared the response to seismic loading of various material models, specifically the Drucker-Prager plasticity model [3] and Mazars damage model [4]. Subchapter 4 showed different types of dynamic damping in structural analysis which should not be neglected in transient analyses.
