This study is devoted to the process of formation of a new generation of human rights - a consequence of scientific and technological progress in the field of genetic engineering, medicine, biomedicine, transplantology, reproductive technologies, the emergence of opportunities to change the genome etc. Somatic rights are conceived as a set of rights and freedoms enshrined in the Constitution and international treaties, which give the person the right to dispose of his or her own body, the volume and content of those rights being influenced by ideological attitudes and advances in biomedicine, genetics, transplantology and other sciences involved in human body research. The perception of somatic rights as a category of fundamental rights will contribute to the further consolidation of constitutional law as a fundamental branch, which, in turn, will strengthen the relationship between the science of constitutional law and other legal sciences.