Volcanic eruptions can cause substantial damage and disruption to infrastructure and communities. Contemporary societies typically depend on petroleum infrastructure. Volcanic unrest and eruptions can cause considerable operational and structural challenges for the petroleum sector. The vulnerability of this sector to volcanic hazards is understudied when compared to other potentially dangerous phenomena (e.g. earthquakes). In this paper, we present new volcanic physical vulnerability models for the four key asset classes of the petroleum sector: wells, pipelines, production facilities and storage tanks. The vulnerability models are developed based on a literature review and facilitated expert judgement in the form of workshops with petroleum engineers and volcanic risk experts. These models consider four hazard intensity metrics (burial thickness, static load, dynamic pressure and airborne ash concentration) and are thus applicable to multiple volcanic hazards. We apply these models to pre-existing multi-hazard eruption scenarios for Taranaki Mounga volcano in Aotearoa New Zealand, using an available impact assessment framework to demonstrate their usability in impact and risk modelling. Our impact assessment indicates that a future eruption of Taranaki Mounga volcano could cause widespread impacts to the petroleum sector, which would in turn create a prolonged national emergency due to energy supply shortages for major industries and consumers. These vulnerability models may be applied in other volcanic regions worldwide to inform risk reduction and readiness actions.