Security of retirement system is one of the elements of social security system. Demographic changes have necessitated changes in the pension system. The reformed pension system is based on three pillars, but the third one, based on voluntary savings is of much less importance than expected. There is no interest but the conditions for the use of this pillar. Conditions necessary lie primarily in cash, its deterioration and lack of institutional capacity for stable growth of savings. There is no interest in the public but there are no conditions for the use of this pillar. However, the ratio of the first pension to last salary may be much lower than it was in the previous system. It is expected that this ration is far away from theoretical model of permanent income hypothesis. It is therefore necessary to stimulate private savings for retirement. According to the authors it is a necessity to keep stabilization of monetary system that will make constant the purchasing power of money in the long term. The second necessary condition is institutional possibility to sure constant and relatively high growth of investments.