This study aims to generate a clear and comprehensive description of the students’ competence in the mathematical modeling courses after the lecturers are based on the design task. The students’ competence that will be measured in this research is the competence in constructing mathematical modeling that has been made. In this paper, we will deeply discuss for the competence in constructing mathematical modeling task and validating it. The method used is descriptive qualitative and the subject of this study were 23 students of the 2017/2018 academic year who took mathematics modeling courses. This research starts from the planning stage, namely the analysis of the study of mathematical modeling material, design and validation of research instruments. Furthermore, the implementation phase is taking observation data, interviews and field notes during lectures based on problem development. The last stage of the research is data analysis. The data collection techniques in this study were in the form of observations, interviews, and field notes. The results of this study were obtained descriptions of student competencies in constructing mathematical modeling problems and found misunderstanding of students in interpreting assumptions and variables in mathematical modeling.