Abstract Background Few studies have examined public opinion about the health care system in the former Soviet region. The objective of our study was to evaluate the population’s satisfaction with the health care system and identify factors associated with it in Armenia. Methods We conducted a cross-sectional telephone survey among 576 adult residents of the capital Yerevan using Random Digit Dialing technique. Simple and multivariate logistic regression explored associations between potential determinants and satisfaction. Results A substantial proportion of respondents (45.5%) were dissatisfied or very dissatisfied with the health system. About 49% of respondents negatively evaluated the ability of the system to provide equal access to care. About 69% of respondents thought that the responsibility for an individual’s health should be equally shared between the individual and the government or that the government’s share should be larger. The adjusted odds of satisfaction were higher among individuals with better health status, those who positively rated equal access and respect to patients in the system, those thinking that the responsibility for health should be equally shared between the individual and the government, and those who tended to trust the government. Conclusions This study enriched our understanding of factors that shape the population’s satisfaction with the health care system in different cultural and political environments. We recommend further exploration of public opinion about those system attributes that are not directly linked to patient experiences with care, but might be equally important for explaining the phenomenon of satisfaction.