The ability of velocity methods to describe changesof topology by creating defects like holes is investigated. For theshape optimization energy-type objective functions are considered,which depend on the geometry by means of state variables. Thestate system is represented by abstract, quadratic, constrainedminimization problems stated over domains with defects. The velocitymethod provides the shape derivative of the objective functiondue to nite variations of a defect. Sucient conditions arederived which allow us to pass the shape derivative to the limitwith respect to diminishing defect, thus, to obtain the \topologicalderivative" of the objective function due to a topology change.An illustrative example is presented for a circular hole bored atthe tip of a crack.