PurposeThe continual onset of natural and manmade disasters propels the humanitarian supply chain (HSC) efforts (by organizations, groups and individuals) to always be on a stand-by mode with more and more sustainable solutions. Despite all the sincere and coordinated efforts from all the humanitarian agents and bodies, the likely sustainable outputs are hampered by certain barriers (impediments) which exist at different levels of the HSCs. A better understanding of such barriers and their mutual relationship is deemed helpful in improving the outcomes of humanitarian efforts. Thus, the purpose of this paper is to explore, refine, establish and classify these barriers which thwart the sustainable efforts of the HSCs individually as well as collectively.Design/methodology/approachAn extensive literature review is conducted to identify these barriers which were followed by soliciting the experts’ inputs to update, refine and retain the contextually relevant ones. The opinions about the nine identified and refined barriers are taken from eight experts based in the Northern India who are having at least five years of experience in humanitarian operations. Fuzzy interpretive structural modeling (FISM) is used to examine and establish a hierarchical relationship among these barriers, whereas fuzzy Matrice d’impacts croisés multiplication appliquée á un classment analysis is carried out to further classify these barriers into dependent, autonomous, linkage and dependent barriers.FindingsThe analysis led to the formation of a FISM model where the operational challenges affecting the performance occupy the topmost position in the hierarchy. The results reveal that inconsistent motives, coordination and communication and operational challenges affecting the performance are the dependent, poor strategic planning, capacity-related challenges and poor performance measurement system are the autonomous, and financial challenges, locational challenges and lack of proper awareness are the independent barriers.Research limitations/implicationsThe focus of the researchers was to study and examine these barriers to sustainable HSCs with special reference to the epidemics and pandemics (especially COVID-19), and it sheds light particularly arising during and post disaster phases.Practical implicationsThe structural model contributed by this study is expected to be meaningful for practitioners besides enriching the body of literature. In the context of pandemics, it distinguishes itself from the other available frameworks.Social implicationsAs this research has been carried out in the context of the novel COVID-19, the framework is expected to assist policymakers in comprehending the issues impeding the sustainability of noble humanitarian efforts. Thus, ultimately it is expected to contribute to the ultimate cause of society at large.Originality/valueThis research endeavor distinguishes itself from the other accessible published resources in terms of the specific context, the methodological approach and the nature of respondents. This paper concludes with the practical implications and directions for future research.