One of the fundamental attributes of air power is its ability to attack a significant number of targets at the same time to effect the "strategic paralysis" of an enemy's decision making process. Col John Warden calls this method "parallel attack". But how realistic is it to expect parallel attack to achieve strategic paralysis? This paper describes the potential consequences of parallel attack on the enemy's decision making process and develops new analytical tools to aid planners in planning for parallel attack. Whereas existing parallel attack planning tools focus on the physical features of a command network, the tools developed for this work include both the physical network and the underlying processes. To develop these new tools, a combination of parallel computing theory and decision analysis is used to determine which decision-making processes are most susceptible to parallel disruption. Parallel computing theory forms a large existing body of knowledge on both physical networks and the complexity of performing key processes in parallel. The authors show that certain decision-making models can be significantly disrupted by parallel attack while others may remain relatively intact. A likely progression of decision models is demonstrated as national communications degrade.