Abstract: In order to improve the modeling efficiency for the computational dynamics of the open loop flexible robot, the generalized hybrid recursive dynamics base on the Spatial Operator Algebra (SOA) theory was presented. The generalized flexible robot was described in according to the type of the joint (active or passive). The generalized articulated inertia-matrix, the residual forces and the generalized acceleration and torque were computed through twice tip-to-base recursion and once base-to-tip recursion. At last the O(n) hybrid dynamics was gained. Then the real time solver for the differential-algebra equation was studied based on the linear multi-step method in this paper. Simulations results show that the dynamic modeling and fast integration techniques proposed in this paper are very useful.