Communication networks are vulnerable to natural disasters, such as earthquakes or floods, as well as to physical attacks, such as an Electromagnetic Pulse (EMP) attack. Such real-world events happen at specific geographical locations and disrupt specific parts of the network. Therefore, the geographical layout of the network determines the impact of such events on the network's physical topology in terms of capacity, connectivity, and flow. Recent works focused on assessing the vulnerability of a deterministic network to such events. In this work, we focus on assessing the vulnerability of (geographical) random networks to such disasters. We consider stochastic graph models in which nodes and links are probabilistically distributed on a plane, and model the disaster event as a circular cut that destroys any node or link within or intersecting the circle. We develop algorithms for assessing the damage of both targeted and non-targeted (random) attacks and determining which attack locations have the expected most disruptive impact on the network. Then, we provide experimental results for assessing the impact of circular disasters to communications networks in the USA, where the network's geographical layout was modeled probabilistically, relying on demographic information only. Our results demonstrates the applicability of our algorithms to real-world scenarios. Our algorithms allows to examine how valuable is public information about the network's geographical area (e.g., demography, topography, economy) to an attacker's destruction assessment capabilities in the case the network's physical topology is hidden or examine the affect of hiding the actual physical location of the fibers on the attack strategy. Thereby, our schemes can be used as a tool for policy makers and engineers to design more robust networks and identifying locations which require additional protection efforts.