This research is motivated by the low mathematical reasoning abilities of thrid grade elementary school students. Most students have obstacles to expressing reasons for solving a problem. This means that the students are still experiencing difficulties in making mathematical arguments. This research aims to decrypt the application of Realistic Mathematics Education (RME) model to enhance the ability of mathematical reasoning of third grade elementary school students. By using classroom action research (PTK) method by Kemmis and Mc. Taggart. Participants in this research were third grade students of Public Elementary Schools in Sukasari district of Bandung city, the second semester of 2018/2019 school year, the number of students as many as 21 students. The research starts from the preparation of the RPP, the implementation of learning, observation, and reflection. So it can be concluded the research results from application of Realistic Mathematics Education (RME) model can improve the reasoning abilities of third grade elementary school students.