This work is a compilation of four manuscripts, three of which are published and one is in the second round of review, all in refereed journals. All four manuscripts focus on analysis of stochastic disruptions to support design of capacitated engineered networks. The work is motivated by limited ability to mitigate elevated risk exposure of large-scale capacitated enterprise networks functioning in lean environments. Such inability to sustain enterprise capacity in the face of disruptions of various origins has been causing multi-billion enterprise forfeitures and hefty insurance premiums. At the same time, decision support methodologies for reliable design of dynamic capacitated networks have been largely unavailable. This work is organized as follows. Paper 1 presents a methodology to analyze ca- pacitated healthcare supply chains using a framework of forward ow-matching networks with multiple points of delivery. Special emphasis is given to developing stochastic models for capturing capacity trajectories at the points of delivery. Paper 2 focuses on assuring capacity availability for a critical vertex exposed to random stepwise capacity disruptions with exponentially distributed interarrival times and uniformly distributed magnitudes. We explore two countermeasure policies for a risk-neutral decision maker who seeks to maxi- mize the long-run average reward. We present an extensive numerical analysis as well as a sensitivity study on the uctuations of some system parameter values. Paper 3 extends the capacity assurance analysis for critical vertices by considering stepwise partial system capacity loss accumulating over time. We examine implementation of a countermeasure policy, aimed at reducing the disruption rate, for a risk-neutral decision maker who seeks to maximize long-run average return. We explore how the policy of maintaining the optimal disruption rate is aected by a number of system parameters. Finally, Paper 4 presents a dynamic predictive methodology for mitigation of cross-regional pandemic outbreaks which can be used to estimate workforce capacity loss for critical vertices due to such societal disasters.