Preparedness of technical university's students for solving non-standard mathematical problems can be considered first as a psychological condition that provides an active work, second as a result of special teaching some activity. Non-standard problems are problems that require creative ways of their solving, inventiveness and originality of thinking. The system of non-standard mathematical problems that is used in the author's practice has a personality orientated character as the problems are taken from various areas of science, culture, human life and future professional activity of students. The author offers a methodical algorithm of forming methods of non-standard problems solving directed toward a full-valued forming of scientific cognition methods that take into account student's individuality structure.