The purpose of this research was to find out the increase in the ability to understand mathematical concepts of students who were taught with better Conceptual Understanding Procedures (CUPs) models than students who were taught with convensional model on the material of flat side space in MTsS Dama Puteh. The CUPs models has three stages including: individual, triplets, and class discussions. The author uses an experimental research design with a quasi-experimental design. Sampling was done using population random sampling. In this study all students of class VIII MTsS Dama Puteh. In this study consisted of two classes, namely class VIIIB as an experimental class and class VIIIA as a control class. Data collection using the ability test mathematical concept understanding of the results showed that based one the t-test obtained tcount = 1,8 and ttable = 1,68. Because tcount > ttable so that it can be concluded that the increased ability of understanding mathematical concepts of students taught with more CUPs models better than students who were taught with convensional models on the material to build flat side spaces in MTsS Dama Puteh.