Supply chains are becoming more and more uncertain. It is more relevant now than ever to plan and model supply chains to handle such uncertainties. This paper designs a supply chain network for medical oxygen under uncertain demand. The paper tackles the complex logistical challenge of managing emergency medical supplies of medical-grade oxygen in the scenario of a pandemic. A facility location problem considering scenario-based uncertain demand is formulated using two-stage stochastic programming. An inventory distribution problem is next formulated to model the flow of medical oxygen in multiple periods to provide maximum service to medical facilities when the available transportation capacity is finite. The model includes various aspects that reflect the scenarios originating in a pandemic, such as limited vehicle availability, limited production capability, uncertain demand, etc. A scenario-based stochastic approach is considered to include the uncertainty aspect of a pandemic scenario. The proposed methodology was studied using two numerical analyses. The results show that, as the number of cryogenic vehicles available was finite, having buffer facilities such as cryogenic tanks to store liquid oxygen helps absorb demand variations in a pandemic scenario. A greater number of medical facilities can be serviced with fewer storage facilities, which can be very crucial in a pandemic scenario. Considering the need for swift planning required in emergency scenarios, the results will be useful for managers, practitioners, and academicians to make supply chains more resilient to risks and uncertainties.