In real life many agencies are using the flexible foundation as a base of support, such as ship hull or deck, the chassis of car, and machine tools work on stairs. With the traditional theory, the mathematical model between machine and based simplified as single-degree-of-freedom, assuming foundation is a rigid, and many investigate for a single machine, ignoring the dynamic coupling of base and the coupling characteristics between vibrators. This paper build a dynamics model with flexible basis and multiple machines, it’s multi-degrees-of-freedom model. The foundation is flexibled. On this basis builiding a model about multiple machines, flexible foundation and vibration isolation system. This paper resolve to the problem of the machine work on stair, research the system include vibrator, actuators, and flexible foundation. Using Lagrange equation deduce dynamics equation. Express every factor in eqution,deduced the state and space expression.Take prepare for optimal and system simulation.