This paper presents a new and general technique for solving the inverse dynamics of open loop flexible multibody. The inverse dynamic of flexible multibody is defined as to solve the generalized forces which applied on joints and the special force in terms of the generalized linear velocity、generalized angular velocity、generalized acceleration of robots end-effector and the mass matrix of the system. This paper uses operator to develop new spatially recursive inverse dynamics algorithms for loop flexible multibody systems. Compare to O(n3) inverse dynamics algorithms，this algorithm was O(n). In order to show the performance and accuracy of the proposed method，the paper presents simulation analysis for different multibody and several trajectories. When available，the results are compared with those published in previous literature.