The urgency of the problem under investigation is due to the role of mathematical modeling in modern science and human practice, which requires the acquaintance of students with the elements of this process at the early stages of education. Training of mathematical modeling shows the students how to apply mathematics in real life, which is also a motivation for learning the subject. The purpose of the research is to identify elements of mathematical modeling that can and should be appropriately formed at the secondary school. The leading method of the research is the analysis of the structure of the mathematical modeling process and the development of a system of tasks aimed to form training activities that are adequate to the identified elements. The authors offer to use the system of changed tasks contained in school mathematics textbooks. The article proves the necessity of acquaintance of schoolchildren with the structure of the process of mathematical modeling, features of models, purpose of their use. As a result of the research, the authors present a model of the system of problems aimed to form elements of mathematical modeling relating to the stages of formalization and interpretation. The methodology proposed in the article can be used by mathematics teachers at lessons and elective courses, authors of textbooks and manuals, and also can be the basis for special courses for students of pedagogical universities.