When applied loads vary with time, inertial effects cannot be neglected and, sometimes, they are more significant than deformation. In such cases, we need to compute the dynamic equilibrium, which is the topic of Chapter 6. Structural dynamics analyze how structures behave under time-varying loads, like vibrations, earthquakes, or impacts. In dynamics problems, the inertial terms are always linear due to the conservation of mass in the Lagrangian description. When structural response is a nonlinear function of displacements, it is referred to as nonlinear dynamic analysis. Therefore, nonlinearity comes from structural static response, not from inertial effects. The good news is that rigorous theoretical studies in linear dynamics can still be applicable for nonlinear dynamics, including stability and convergence. In Sect. 6.2, the dynamic analysis of linear systems is briefly presented because most theories in this section can still be applicable for nonlinear dynamics. Structural dynamic equations are written in the form of ordinary differential equations in the time domain, which need to be integrated to describe the dynamic behavior of the system. Since the modal superposition method requires constant mass and stiffness matrices, it is not applicable for nonlinear dynamic problems. For most nonlinear systems, the dynamic response is obtained by direct time integration of the finite element model. Section 6.3 presents numerical time integration methods for linear systems, and Sect. 6.4 for nonlinear systems. The variety of numerical integration methods can be categorized into the implicit and explicit methods. The former requires convergence iteration, while the latter does not. It is important to understand different numerical time integration methods from the perspective of stability and convergence.