Various types of 5-axis machine tools have been developed. In the case of a machine tool composed from linear motion, the kinematic equation can be obtained easily and intuitively. However, machine tools with more than four axes, including rotating axes, have generally performed kinematic and dynamic performance analyses using mathematical methods. In this paper, the kinematic equations of various types of machine tools are obtained, based on the Homogeneous Transformation Matrix method. The loop stiffness was then calculated as a mathematical model. A mathematical model of loop stiffness was verified by using a method to calculate the loop stiffness of a commercial program. The results of the mathematical model showed less than a 1% error with the commercial program, and this could show the validity of the mathematical model. Then, this model was applied to two types of machine tools. The minimum loop stiffness of both models is compared.