Researchers chose a modified free inquiry model to help improve students’ fluency and elaboration. The purpose of this research is to know the application of modified free inquiry which can improve the student’s fluency and elaboration of students’ thinking on trigonometric material. Research method in this research is qualitative research method and research type is research of class action. The data in this study were obtained from the results of validation, test results, observation of teacher and student activity, and interview result, then apply data triangulation and theory to check the validity of data. The results showed an increase in fluency and elaboration in students. This means that a modified free inquiry model can help improve students’ fluency and elaboration in trigonometric learning. The results are supported by the observation of teacher and student activity that is in accordance with the lesson plan and also the result of the interview which get positive response from the students.Keywords: modified free inquiry, fluency and elaboration, mathematics