Generation Z presents people born after 1995 and is also called digital generation, generation of media and generation.com. Its members have specific attitudes and expectations as consumers, employees and citizens. They are the youngest consumers who participate on labour market. Also, they have specific savings habits and a level of financial literacy. To understand how members of Generation Z are saving, their attitudes towards saving and their own financial capacity, a research was conducted using a survey questionnaire on a suitable sample of 250 respondents, adult members of Generation Z born between 1995 and 2001. Examined variables relate to attitudes towards savings, their own financial capacity and tendency to save. It is concluded Generation Z has positive attitudes towards saving, believe they can make their own financial decision and have tendency to save. Most of Generation Z is saving and mostly by themselves, not in the bank. They are familiar with types of saving available on the market, but they do not use them on a larger scale. To raise the number of savings in banks and in general, and to increase awareness of saving between young adults of Generation Z it is necessary to enhance their knowledge about personal finances and saving strategies and to adjust saving offer according to their needs.