This study highlights that earthquakes can lead to short-circuit faults, power outages, and equipment damage in distribution systems. Based on the observation of the effects of two major earthquakes that occurred in Turkey (February 6, 2023), a new analytical model for strengthening distribution systems against natural disasters is proposed in this study. In this model, the distribution system is analyzed, and the fragility index of the buses is determined. The technical condition of the distribution system is assessed using fragility indexes, and integration and sizing of Distributed Generation (DG) and energy storage units are performed to ensure energy continuity after an earthquake. This fragility index takes into account both the operation of the distribution system in island (microgrid) mode and its operation connected to the main grid. In addition, with the fault index recommended within the scope of the analytical model, the vulnerable points of the distribution system against short circuit faults are analyzed and short circuit fault currents are limited at these points. Thus, the resilience of distribution systems against natural disasters such as earthquakes can be enhanced with the proposed analytical model.