Resilience is the human capacity to adapt to adverse life situations; it can be enhanced by the action of various protective factors and one of the most important of these is social support. The objective of this study was to identify associations between resilience and sociodemographic variables (gender, age, income, marital status, housing arrangements and religion), as well as correlations between resilience and social support in a sample of 86 urban elderly people. A sociodemographic questionnaire, the Resilience Scale and the Social Support Scale were used. The mean age was 75.7 years (SD = 5.35), with a predominance of women (72.1%, n = 62). A high level of resilience (M = 134.37, SD = 16.6) and a moderate level of social support (M = 17.36, SD = 2.77) were observed in the elderly people. There was only a significant association between resilience and religion (χ2 = 0.30; p = 0.027). Only a weak and positive correlation was observed between the factor of independence and determination on the Resilience Scale with social support (p = 0.005). Linear regression analysis revealed that social support was not a predictive variable for the capacity of resilience in the researched group. It is necessary to create new research instruments that permit a more precise study of the protective effects of social support regarding the capacity for resilience in the elderly.