High computational efficiency of spacecraft docking dynamic simulation is needed for analysis based on a great number of random initial conditions, and sometimes for real time simulation. From the point of view of this dynamical process, a docking mechanism with many kinematical loops, in spite of its low mass, is more complex than a spacecraft. Some efficient simulation algorithms for such a class of mechanical systems are considered in this paper. For efficiency purposes, they are realized using a specialized symbolic manipulation system. Before simulation, a multi-loop mechanical system is transformed to a tree structure using constrain equations instead of individual joints. This paper states that a possibility of partitioning kinematical loops to controlled and dependent kinematical chains, and a limited number of structure types of the latter are typical for docking mechanisms. This paper proposes a modification to the Composite Rigid Body Algorithm (CRBA) for a transformed tree structure mechanical system with a moving base, and an additional recursive algorithm for the calculation of the force and moment acting on this base. Both of these supplements to CRBA allow linking of separate dynamic equations of a spacecraft and a mechanism. The Articulated Body Algorithm (АВА) is applied to partially open kinematical chains without kinematical loops, which occur in some central type docking mechanisms (the probe-cone type). The АВА calculates by itself the force and moment acting on the mechanism base and the spacecraft.