This research was conducted because of the students' low ability to solve mathematical problems. The aim of this research is commited to increase the mathematical problem solving abilities of VIII E students in second semester of SMP Negeri 2 Sewon academic year of 2018/2019 using the Rigorous Mathematical Thinking (RMT) learning approach. This type of research is Class Action Research (CAR). This research consists of two cycles where each cycle consists of three meetings. The subjects of this study were students of class VIII E, amounting to 30 students, consisting of 20 male students and 10 female students. The object of this research is students' mathematical problem solving abilities using the RMT approach. Data collection techniques used in the form of observation instruments, tests, interviews. Data analysis techniques were carried out by qualitative descriptive analysis. The results showed that learning with the RMT approach can improve students' mathematical problem solving abilities. The results of the analysis of cycle test assessment sheets in Cycle I percentage of students' ability to solve problems was 65.56% with sufficient categories. While the results of the analysis of cycle test assessment sheets in Cycle II the percentage of students' ability to solve problems was 79.72% with good categories. From these results there was an increase in students' ability to solve mathematical problems by 14.16%.