The measuring space is the set of positions a flexible arm coordinate measuring machine (FACMM) can reach, and it is an important measure for the evaluation of a FACMM. To study the measuring space of FACMMs the kinematic model was established. Furthermore, a new method based on Monte Carlo method to calculate the measuring space of FACMMs was proposed. The method generates the data of joint angles with Monte Carlo method, which is used to calculate the coordinates of the FACMM’s probe through the kinematic model. These coordinates make up the measuring space. The results of the analysis on the measuring space show that the measuring space of FACMMs is not a sphere usually considered as but an ellipsoid, and there is lack of flexibility near the border of the measuring space.