BEIJING—China's elderly are poor, sick and depressed in alarming numbers, according to the first large-scale survey of those over 60, an immense challenge for Beijing and one of the greatest long-term vulnerabilities of the Chinese economy.

The survey of living conditions for China's 185 million elderly paints a bleak picture that defies the efforts of the government to build what it calls a "harmonious society," one dedicated to human welfare rather than simply economic growth. Of the generation that built China's...