Of machine tool - foundation - ground-coupled vibration analysis. This paper in response to the special needs of large machine tools to construct a mathematical theory, the theoretical foundation of better integrated into the overall framework, so the infrastructure can reduce the vibration and thus improve the precision and stability. This analysis of three parts to: (a) to solve the vibration of single degree of freedom in the upper and lower coupling for the change of the soil; (b) establishing the basis of the concept of freedom has been advanced with more than six derived changes in the direction of vibration; (c) will establish a comprehensive theoretical and numerical simulation for comparison. Finally, with simulation and theoretical analysis of important parameters of the coupled model static and dynamic effects.