This paper studies the impact of an unfunded social security system on the distribution of bequests in a framework where savings are due both by life cycle and by random altruistic motivations. We show that the impact of social security on the distribution of bequests depends crucially on the importance of the bequest motive in explaining savings behavior. If the bequest motive is strong, then an increase in the social security tax raises the bequests left by altruistic parents. On the other hand, when the importance of bequests in motivating savings is sufficiently low, theincrease in the social security tax could result in a reduction of the bequests left by altruistic parents under some conditions on the attitude of individuals toward risk and on the relative returns associated with private saving and social security. Some implications concerning the transitional effects of introducing an unfunded social security scheme are also discussed.