Engineering structures are sometimes subject to extreme loading events like vehicle impact, gas explosions, fire or terrorist bombing. These events are characterized by very small probabilities of occurrence, but large effects on design loads. Extreme loading events are also characterized by large uncertainty: impact load changes significantly with vehicle mass and speed, explosion pressure waves depend on charge distance and size, etc. Due to large uncertainty in possible loading scenarios, it is often considered that such extreme events may lead to complete loss of load-bearing elements like walls, beams or columns. In this context, the decision to design or strengthen a structure to support eventual loss of a load-bearing element is a typical example of decision making in presence of uncertainty, with obvious impacts on construction costs. In this chapter, we address the cost-benefit of strengthening structures to withstand loss of load-bearing elements. We show how this decision is rooted on the probability of losing the load-bearing element, which should be the result of a risk analysis addressing a structure’s adjacency, ownership and intended use. We also discuss how this decision depends on the aspect ratio of buildings, on strengthening costs, and on the extent of strengthening measures.