The education curriculum that was updated 2011 aims at the acquisition of basic mathematical knowledge, the development of mathematical-considered communication, and rational problem-solving ability with respect to society, natural situations, etc. Through mathematical modelling, students can become aware of the basic structure of situations around them, search through interesting topics, understand the importance of mathematics, and reinforce rational thinking about the useful skills needed in their lives. The purpose of this study was to analyse students' modelling processes and the roles of mathematical thinking step by step. The conclusion of this research is as follows. First, a visual-thinking-style student used both mental representation of the situation and real model steps. On the other hand, an analytic-thinking-style student frequently used a mathematical model and demonstrated a more complicated way of solving a problem than a visual student. Second, critical thinking from the modelling process was used for filtering the conditions from real modelling step and reasoning of mathematical result from mathematical model. The students used inductive reasoning in the investigation and the extra-mathematical knowledge that is needed in the model solving process. They also used deductive thinking when they proved the validity of their models.