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This paper presents a two-stage hybrid robust programming model that integrates multiple blood products scheduling and multiple casualty types evacuation under facility disruptions risk and casualty number uncertainty. The model seeks to maximize the rescue efficiency and minimize the total operations cost. Under a set of disruption scenarios, we adopt a scenario-based robust method to address disruption risks at temporary medical centres and two robust uncertainty sets to deal with uncertain casualty numbers. We propose a proximal bundle algorithm to solve large-scale instances of the proposed hybrid robust model approximately. Extensive numerical experiments show that: (i) the trade-off between model robustness and solution robustness can help the decision-makers determine an appropriate risk-aversion weight; (ii) compared with the corresponding stochastic and scenario-based robust models, the hybrid robust model can obtain more robust solutions with a slight increase in cost; (iii) the proximal bundle algorithm can produce near-optimal solutions within reasonable computational times; (iv) some model parameters have significant impact on the total cost, which can help decision-makers set the appropriate parameters to achieve the desired outcome. Finally, we also use the real data of the 2008 Wenchuan County Earthquake in Sichuan Province, China, to illustrate the application of the model. • An HRM is developed for jointly plan blood logistics and casualty evacuation. • The model considers facility disruptions risk and casualty number uncertainty. • A PB algorithm based on Lagrangian relaxation is proposed. • Experiment results show that HRM outperforms the SM and SRM. • Real data are used to illustrate the application of the model. [ABSTRACT FROM AUTHOR]