Emergency departments (EDs) provide health care services to people in need of urgent care. Their role is remarkable when extraordinary events that affect the public, such as earthquakes, occur. In this paper, we present a hybrid framework to evaluate earthquake preparedness of EDs in cities. Our hybrid framework uses artificial neural networks (ANNs) to estimate number of casualties and discrete event simulation (DES) to analyse the effect of surge in patient demand in EDs, after an earthquake happens. At the core of our framework, Earthquake Time Emergency Department Network Simulation Model (ET-EDNETSIM) resides which can simulate patient movements in a network of multiple and coordinated EDs. With the design of simulation experiments, different resource levels and sharing rules between EDs can be evaluated. We demonstrated our framework in a network of five EDs located in a region of which is estimated to have the highest injury rate after an earthquake in Istanbul, Turkey. Results of our study contributed to the planning for expected earthquake in Istanbul. Simulating a network of EDs extends the individual ED studies in the literature and furthermore, our hybrid framework can help increase earthquake preparedness in cities around the world. On the methodological side, the use of ANN, which is a member of machine learning (ML) algorithms family, in our hybrid framework also shows the close links between ML and DES.