I study how the distribution of wealth influences the government´s response to a banking crisis and the fragility of the financial system. When the wealth distribution is unequal, the government´s bailout policy during a systemic crisis will be shaped in part by distributional concerns. In particular, government guarantees of deposits will tend to be credible for relatively poor investors, but may not be credible for wealthier investors. As a result, wealthier investors will have a stronger incentive to panic and, in equilibrium, the institutions in which they invest are more likely to experience a run and receive a bailout. Thus, without political frictions and under a government that is both benevolent and utilitarian, bailouts will tend to benefit wealthy investors at the expense of the general public. Rising inequality can strengthen this pattern. In some cases, more progressive taxation reduces financial fragility and can even raise equilibrium welfare for all agents.