Aim is to formulate and analyze a new psychological problem where the subject’s understanding of events that can be characterized as impossible. Methodology. The problem is solved with use of the psychology of the possible. The relevance of this problem is proved by the few studies of the impossible I, alternative life stories, the need for the transcendental, which contradict to everything real, which already exist in psychological science. The impossible is analyzed as an integral component of the existential experience of the subject who understands the world. Results. The classification of categorical features of the discussed phenomenon has been carried out and five meanings of the “impossible” category have been identified. The meanings depend both on objective circumstances and on the knowledge and expectations of the knowing subject: the contradiction between the logically permissible and the physically unacceptable; “causelessness” of the event; implausibility; the unknown as impossible; meaninglessness of “situations of impossibility”. Research implications. In the article analyzes the understanding of impossible events and situations from the point of view of a new area of psychological research - the psychology of the possible. Its development is necessary to improve the methods of enumerating alternatives in artificial intelligence, the psychological study of life options and other areas of human existence.