The mathematical critical thinking process is a student's thinking ability in analyzing and evaluating information to reach valid conclusions. In solving mathematical problems, critical mathematical thinking process skills are needed for students to solve more difficult problems. The application of scaffolding is considered appropriate to help slowly improve their mathematical critical thinking process abilities until they are finally able to solve problems independently. This research uses a qualitative approach with descriptive research type. The subjects determined in this research were four Darussolah Singonjuruh High School students who had been selected by mathematics teachers at the school, with details of 2 students with high abilities and 2 students with medium abilities. Data collection was carried out by conducting tests before and during the scaffolding, and accompanied by interviews. Data analysis is carried out interactively and continues until saturation. The research results obtained before scaffolding showed that there was only one subject who could complete it well. Then, through scaffolding the abilities of the four subjects slowly increased to fulfill the four stages of the thinking process being studied and the percentage scores for the four subjects were achieved. Providing scaffolding is considered to be able to improve students' thinking processes in solving problems regarding two-variable linear equation systems.