This article estimates the effects of 50 years of steady growth in incomes on poverty rates among the elderly. It assumes that the poverty threshold continues to be adjusted for inflation but not for increases in real incomes. Simulations with the March 1998 Current Population Survey indicate that if the benefit rules for Social Security and Supplemental Security Income (SSI) are not changed and if earnings and other sources of income in an otherwise unchanging population grow by 1 percent per year (the intermediate assumption about earnings growth used in the Social Security Trustees' Report), poverty among the elderly will decrease from 10.5 percent in 1997 to about 7.2 percent in 2020 and to 4.1 percent in 2047. These projected poverty rates are quite sensitive to both the assumption about earnings growth and the assumption that benefits are not further reduced to maintain solvency. This article quantifies the sensitivity of the results to these assumptions and discusses several other aspects that might affect future poverty rates--changes in other income components like SSI, earnings, and pensions; changes in longevity and marital patterns; and changes in the distribution of earnings.