In 2000, 8.8 million children received food stamps, making the Food Stamp Program a crucial component of the social safety net. Despite its importance, little research has examined the effect of food stamps on children's overall well-being. Using the Current Population Survey from 1989 to 2001, we consider the impact of food stamps on three measures of poverty - the headcount, the poverty gap, and the squared poverty gap. These measures portray the incidence, depth, and severity of poverty. We find that in comparison to the headcount measure, food stamp benefits lead to large reductions in the poverty gap and squared poverty gap measures. We then simulate the effects of several changes in the distribution of food stamps and find that a general across-the-board increase in benefits has little impact on poverty reduction. In contrast, targeted changes can greatly reduce the depth and severity of poverty - increasing benefits to the poor results in a greater reduction in the depth of poverty than expanding participation rates, at a similar cost, among poor households.