The paper addresses the questions of demographic ageing at the beginning of the 21st century and the attitudes about who should be responsible for the elderly care in Lithuania. The analysis of age structure changes revealed three ways of demographic ageing: ‘from below’ (the youngest part of the population is decreasing), ‘from above’ (the oldest part of the population is increasing), and decrease of the young working-age population. The analysis of ageing in Lithuania in the context of the EU revealed that Lithuania has moved from the group of the demographically youngest countries to the group of the oldest ones. This has happened in one decade and illustrates rapid ageing in Lithuania. Within such context, the question “Who should be responsible for the elderly care?” is of particular importance. Based on the second wave of the Generations and Gender Survey (conducted in 2009), the responses who should take care of the elderly are contradictory. The biggest part of respondents is in favour of the division of responsibilities for the elderly care between family and society. The same part of respondents considers this to be family responsibility. Meanwhile, financial support is mainly considered to be the responsibility of the society. The analysis of filial responsibilities for elderly parents revealed a high level of normative solidarity. Most respondents agree with the statement where the support type for elderly parents is not defined (i.e. that children should take responsibility for caring for their parents when parents are in need). When the types of support are defined, the respondents are also likely to agree (i.e. children ought to provide financial help for their parents when their parents are having financial difficulties; children should have their parents to live with them when parents can no longer look after themselves). Less agreement was found on the statement requiring the reorganisation of children’s lives in order to fulfil filial responsibilities (i.e. that children should adjust their working lives to the needs of their parents) and on the statement measuring gender division in care provision for elderly parents (i.e. when parents are in need, daughters should take more caring responsibility than sons). The differences in attitudes between children’s, parents’ and grandparents’ generations were not statistically significant. The logistic regressions revealed that significant predictors enhancing the chances of agreement on filial responsibilities are respondents’ gender, age, partnership and occupational statuses and type of residential area.