The major theme of this thesis is focused on the problem of power integrity. Power integrity is a crucial issue to the stability of entire system. As noticed of the ground bounce noise for the primary noise of power-ground planes, it comes from the transition of signal current through a via which radiates the electromagnetic waves between planes. In order to avoid the voltage fluctuation, leading to misjudgment of digital signal, this thesis combines the genetic algorithm with the triangular-mesh scheme to model the power-ground planes, and thus optimizes the placement of decoupling capacitors on the specified locations for a realistically irregular-shaped geometry. This thesis discusses the low-frequency responses of multi-layered structures using a simple model which describes the effect of shorting vias on power integrity. Finally, the design rule of the placement of shorting vias is proposed to maintain the power integrity of multi-layered structures.