Deep uncertainty usually refers to problems with epistemic uncertainty in which the analyst or decision maker has very little information about the system, data are severely lacking, and different mathematical models to describe the system may be possible. Since little information is available to forecast the future, selecting probability distributions to represent this uncertainty is very challenging. Traditional methods of decision making with uncertainty may not be appropriate for deep uncertainty problems. This paper introduces a novel approach to allocate resources within complex and very uncertain situations. The resource allocation model for deep uncertainty (RAM-DU) incorporates different types of uncertainty (e.g., parameter, structural, model uncertainty) and can consider every possible model, different probability distributions, and possible futures. Instead of identifying a single optimal alternative as in most resource allocation models, RAM-DU recommends an interval of allocation amounts. The RAM-DU solution generates an interval for one or multiple decision variables so that the decision maker can allocate any amount within that interval and still ensure that the objective function is within a predefined level of optimality for all the different parameters, models, and futures under consideration. RAM-DU is applied to allocating resources to prepare for and respond to a Deepwater Horizon-type oil spill. The application identifies allocation intervals for how much should be spent to prepare for this type of oil spill and how much should be spent to help industries recover from the spill.