Reasonable and timely prediction of the number of earthquake casualties is crucial to reduce the risk of severe earthquake casualties. Good real-time predictions help government decision makers make informed emergency rescue decision in a timely manner. To provide timely predictions of casualties for an early rescue planning, we only consider factors available to government agencies early on. These factors include earthquake magnitude, aftershocks, population density, depth of epicenter, time of earthquake and location of epicenter. Casualties caused by earthquakes of similar magnitude often vary greatly from region to region; however, the types of death, serious injury and minor injury, associated with each earthquake are highly correlated. Therefore, we consider a joint Poisson mixed model for death, serious injury and minor injury, in which earthquake-specific random effects can help capture the uncertainty between earthquakes and characterize the positive correlation between the three types of casualties. Furthermore, we have applied this method to analyze the casualty data in two very different regions. The first one is Yunnan province which is a region of frequent earthquakes in China, and the other is Indonesia, a country with frequent earthquakes. In both cases, our method provided good estimates for the numbers of death, serious injury and minor injury simultaneously. In addition, the predicted random effects associated with our method not only help identify anomalous earthquake casualties, but also provide a basis for probabilistic prediction of severe casualties.