The article substantiates the integrated character of reading competence, clarifies and deepens its concepts and features in the process of teaching Ukrainian literature. The issue of the article is actualized in the context of the competence orientation of the New Ukrainian School (NUS). Reader's competence is explained as an integrated component of students' academic achievement, a system of knowledge and skills, values, perceptions and attitudes of the individual, the ability to adequately act in the future professional field and different life situations. The level of this competence determines the depth of reading the work and understanding its content and meaning, is an indicator of personality development. It is proposed to distinguish the reader's competences related to conscious and expressive reading of the work, the cognitive, which depend on the intellectual and emotional activity of students over the text, communicative, filling the reader's work with broad subject connections, and value related to comprehension of the influence of what have been read on the character of the reader. The way of forming reading competence in the process of working on the text of a literary work is highlighted: a) fast and expressive, conscious reading of the work, its rereading and retelling; b) analysis and characterization of the figurative components of the work in their interaction; c) deducing figurative and conceptual generalizations from what have been read. Reader's competence is presented as a concept, each component of which relates to the appropriate stages of students' work on a work of art. Synonymic connections between the concepts of reading, subject and literary competence are revealed, which is in line with the features of the competent reader as defined in the renewed school curriculum for literature (2017). Important conditions for the formation of a competent reader are the continuous development of his interest in literature, interested reading of works of fiction, scientifically grounded literary analysis and awareness of the personal meaning of the work that have been read. The system-structural approach to the formation of pupils' reading competence which provides the purposeful application of the system of teacher's educational actions not only in the content of a particular work, but also in the ways of reading activity over its text is approved.