The topicality of the investigated problem is stipulated by the social need for training competitive engineers with a high level of graphical literacy; especially geometric and graphic training of students and its projected results in a competence-based approach; individual characteristics and interests of the students, as well as methodological approaches to the design of training and methodological support of the process of individualization of geometric and graphic training. The purpose of the article is to develop a structural and functional model of organization of geometric and graphic training of students of a technical University and its approbation. The leading method of research of this problem is a pedagogical modeling, which allows to consider this issue as a process of developing students readiness to operate spatial objects in the study of geometric and graphic disciplines. The article presents the structural and functional organization model of geometric and graphic training of students in technical university, consisting of interrelated components: a target, theoretical and methodological, technological, diagnostic and effective; we developed an algorithm for the implementation of this model. The article can be useful for the organization of the geometric and graphic training in universities, with appropriate adaptation in educational institutions of secondary vocational education in specialized classes in secondary schools.