In this study, Shannon's entropy and the TOPSIS techniques have been used for ranking residential areas against the earthquake hazards. For this purpose, 8 variables were examined in 27 districts of Amol city. These variables include released energy, earthquakes of the last 20 years in terms of ton TNT, buildings quality, residential density, building density, population density, network permeability, urban open space, and groundwater depth after construction. Information was ranked based on the proximity to the ideal vulnerability ideal using the Shannon entropy and the TOPSIS multi-character decision model. The rankings obtained from this analysis were added to the city map and the areas of the city were divided into five categories with vulnerability, including ‘ too much’ , ‘ much’ , ‘ medium’ , ‘ little’ , and ‘ too little’ and finally the map of the extent of Amol's vulnerability was prepared. The results showed that the central areas, i. e. 24, 13, 18, 10, and 12, are very vulnerable. Moreover, areas 19, 17, 14, and 16 are highly vulnerable, areas 15, 21, 2, 6, 22, 25, 11, 20, 27, and 4 have moderate vulnerability, areas 26, 9, 23, 3, 1, and 5 have low vulnerability, and finally, areas 8 and 7 have very vulnerable to earthquakes, respectively. Therefore, it is expected that the vulnerability of urban areas will be considered in future constructions.