Earthquakes put heavy strains on hospital systems during the disaster emergency response phase. Damage to hospitals and supporting infrastructure disrupts critical hospital functions and damage to the built environment in the hospital's catchment community causes injuries that require medical treatment. As a result, a compromised hospital system can result in decreased "supply" as "demand" increases. These two components are key to the analysis of hospital-system resilience in earthquake-prone areas. This study (1) examines relevant techniques to assess both multiseverity earthquake casualties and loss of hospital functionality following earthquakes, (2) provides a method for combining casualty and hospital functionality estimation to assess the earthquake resilience of the hospital system, and (3) highlights the importance of these outputs for emergency planners and other stakeholders in order to enhance the resilience of cities. An illustration of the methodology is included through an application to the city of Lima, Peru, subjected to an 8.8 Mw earthquake.