Morality, being a system of values by which people determine the (im)propriety of thoughts and actions, is relative and depends on the specific society and time period. A large number of studies by philosophers, sociologists, psychologists, economists and lawyers are devoted to the moral state of modern Russian society. In the present paper, we investigate this subject by the methods of computer linguistics. The article analyzes the frequency dynamics of words belonging to the semantic group “morality, duty, conscience” in the Russian language during the 20th − the beginning of the 21st century. The words for analysis are selected from dictionaries, as well as based on semantic proximity determined by vector semantics methods. The methods of mathematical statistics, computer linguistics are applied to the Google Books Ngram corpus that contains 80 billion words of the Russian language, as well as to the Russian National Corpus. The Google Books Ngram data are first processed by a reasoned algorithm of frequency dynamics correction. The words from the above semantic group, which significantly change their frequency, as well as time intervals of the most significant changes in frequency trends are singled out. Some correlations of linguistic markers of the moral state of society with crisis periods, negative individual and collective experiences, and the dynamics of group identity are revealed. The methodology can be applied to different semantic groups and languages. The results confirm the correlation between the dynamics of word frequencies in the Russian language and socio-psychological processes in the society.