Emergency medical service (EMS) is important for rescuing victims suffering from life-threatening illnesses or accidents, and is highly time-sensitive by nature. Many uncertain contexts in the urban environment can prolong EMS response time and deteriorate its performance. Using the enhanced two-step floating catchment area (E2SFCA) method, this study measures EMS accessibility with the effect of a regular uncertain context (i.e., the city dynamics like time-varying population and traffic) and an irregular uncertain context (i.e., an extreme pluvial flood event which can cause extensive road closures). The results indicate that, in the central urban area of Shanghai, mid-west areas with denser populations have higher accessibility than eastern peripheral areas. Flooding can cause a remarkable decline of accessibility which falls to the lowest point slightly earlier than the time when the worst road connectivity emerges. The night time exhibits better accessibility than especially the peak hours during the daytime. The GWR results reveal that increasing facility richness and road density while decreasing flood-induced road closures have a positive effect on EMS accessibility. The study indicates that both regular and irregular uncertain contextual factors can influence EMS accessibility in a highly complex manner. Carefully taking these uncertainties into account would enable EMS planning in other contexts and regions to face the enormous challenges posed by the changing climate and increasingly complex urban environment.