Abstract: The treeshaped holonomic multi-rigid-body system, subjected to outside first order linear non-holonomic constraint, is regarded as treeshaped non-holonomic multi-rigid system. The rigid-body with symbol 1 is linked with the ineftial reference frames by the virtual joint 1, therefore the shock motion equations on treeshaped non-holonomic multi-rigid-body system can be obtained using the method given in reference 1. An example is provided which verifies the correctness of the present approach.