As we have seen in various formulations of structural optimization in Chap. 1, the sensitivity coecients of responses with respect to the design variables are needed for obtaining optimal designs using a gradient-based nonlinear programming approach. In this chapter, we rst present an overview of sensitivity analysis in Sec. 2.1. The static and eigenvalue sensitivity analyses are presented in Secs. 2.2 and 2.3, respectively. Methods for linear buckling load, transient response, and geometrically nonlinear response are brie y presented in Secs. 2.4, 2.5, and 2.6, respectively. Finally, shape sensitivity analysis of trusses is presented in Sec. 2.7.