Due to the increase in the number and severity of disasters, managing the injured people immediately after a sudden-onset disaster is essential when there are limited resources, such as search and rescue and medical teams. These people are classified into the four triage groups. Uncertainty is an inevitable element in the chaotic environment after the disaster. This paper develops a robust stochastic optimization model to allocate the limited resources to the affected sites and casualty groups in the early aftermath of sudden-onset mass casualty incidents. Search and rescue operations and temporary treatment are considered in the model. Link disruption and facility unavailability in a dynamic environment are considered to make the model realistic. The robust model tries to maintain the optimal solution under given scenarios that are close to its expected value. We incorporate model and solution robustness in the model simultaneously. Numerical analysis experiments on the model performance, and the results are presented.