Mathematical model is the result of people's abstraction and formalization of objective things, and it is a mathematical description of the internal essence and development law of objective things. With the rapid development and wide popularization of computer technology, the significance of mathematical modeling has become increasingly prominent, and mathematical modeling has become an important means and way of natural science and humanities and social science research. However, compared with the vigorous development of mathematical modeling research in the application field, the teaching and research of mathematical modeling are relatively backward, and the psychological research of mathematical modeling is one of the weak links. Therefore, based on the information processing theory, this study explores the basic psychological process and its influencing factors of mathematical modeling by referring to the new theories and achievements of cognitive psychology on problem solving, so as to reveal the main cognitive operation components and their relationships in mathematical modeling and understand the characteristics and influencing factors of basic cognitive activities in the modeling process. This study consists of five sub-studies. The basic assumption of the study is that the psychological process of mathematical modeling includes five representational states: real problem information, problem model, mathematical model, solution of mathematical model and solution of real problem, and four cognitive links or stages: language understanding, model construction, model solution and transformation. There are four cognitive links from one state to the next. The research adopts the idea of combining qualitative research with quantitative research, and comprehensively uses research methods such as tests, questionnaires, oral reports and interviews. Taking senior high school students as the object, it focuses on the two basic cognitive links of language understanding and model construction experienced by students from real question information to mathematical model. Through the quantitative analysis of the research data, five main results are obtained: first, the relationship between language understanding and primary mathematical representation and between them and modeling performance has reached a significant level, and deep mathematical representation has a significant effect on improving modeling performance; Secondly, cognitive components such as language understanding, mathematical representation, problem identification, mathematical foundation, and self-monitoring all have effects on modeling results, some of which are direct and some are indirect; Thirdly, the comprehensive ability of mathematical modeling of senior high school students has a steady growth trend from grade one to grade three, in which there are significant grade differences in language understanding, mathematical representation, mathematical foundation and mathematical modeling level, but there are no significant grade differences in problem identification and metacognitive monitoring; Fourthly, the main effect of mathematical model structure factors on modeling results is very significant, while the main effect of problem background factors on modeling results is not significant, and the interaction between background factors and model structure factors is not significant; Fifth, the main effects of familiarity with the problem background and data abstraction on the modeling results have reached a significant level, but the interaction between them is not significant. Through qualitative analysis of qualitative research materials, three main results are obtained: first, language understanding and mathematical foundation are the basis for solving modeling problems, but neither of them is a sufficient condition for modeling success; Secondly, the problem model is a dynamic psychological model, and the information in the model is the result of situational reasoning and representation of the problem information by the problem solver, which has individual differences; Thirdly, both situational reasoning and mathematical reasoning have an important influence on mathematical modeling, which is closely related to students' reasoning foundation. According to the results of qualitative analysis, this part of the study puts forward the idea of cognitive model in the process of mathematical modeling. Based on the above results, this study makes a comprehensive discussion from four aspects: language understanding and its role in the process of mathematical modeling, situational representation and mathematical representation in the process of mathematical modeling, characteristics of selection and transfer of mathematical modeling strategies, and thinking about the basic psychological process of mathematical modeling. The results of this study can enrich people's understanding of mathematical cognition and problem solving, and also provide psychological basis for the teaching practice of mathematical application and modeling. Keywords: mathematical modeling, language understanding, problem solving, representation, model, cognition