Long-term scenarios for mobility within cities usually neglect the energy supply challenge and how the implied risks affect urban mobility services. High levels of private transport and fossil fuel dependency tend to prevail in urban agglomerations of modern cities in many parts of the world. The resilience approach supports a new perspective on transportation solutions, not only based on how to consume less energy or emit less CO2, but how vulnerable urban mobility is in face of a fossil threat. This paper aims to assess the vulnerability of urban mobility in the face of fossil fuel threats under a social and geographical scope. We apply a case study with the city of Rio de Janeiro, confronting city inhabitants with a price increase of gasoline and oil-based public transportation. We found that more than 50% of the districts of Rio de Janeiro presents low-medium or low level of resilience of urban mobility. Furthermore, they are in areas with lower accessibility to metro stations and more citizens with reduced income levels.