This research is conducted due to the problem which is related to the students` inability in mathematical reasoning. Furthermore, the use of problem based learning is considered as one of the tools used to develop the students` mathematical reasoning. The method used in this research is Classroom Action Research (CAR). This method consists of four stages : planning, implementing, observing, and evaluating. This research is aimed to increase students` ability - mathematical reasoning by applying Problem Based Learning model to the students of the first grade of SMA Katolik Santo Bonaventura Madiun that consists of 23 students. This research was conducted in two cycles in which each of the cycle consisted of two meetings.. The data analysis shows that : The average score test in the cycle I : 51,2 and cycle II : 56,. The class completion rate cycle I : 30,43% and cycle II : 47,62%. The average total score which is taken from the data of learning activity in cycle I is 2,92. Hence, it is classified as a good result. Moreover, the average total score in cycle II is 3,36. Thus, it is classified as excellent result. Problem Based Learning (PBL) is considered as the best way to increase the students` mathematical reasoning. Unfortunately, PBL cannot gain a maximum outcome by only depending on II cycles.

Key words: Mathematical Reasoning Ability, Problem Based Learning