To eliminate the shortcomings of manual teaching in the multiple robots cooperative systems for welding, a calculation method for the initial welding point satisfying the global optimal flexibility and the corresponding manipulability-optimal trajectory is proposed based on the kinematics constraint and dexterity. Firstly, the motion constrained relations for multi-robots cooperation is analyzed, then a manipulability evaluation model of multi-robots cooperation systems is put forward. Secondly, the global optimal manipulability is adopted as optimization criteria with the constraint conditions such as collision and singularity. Next, genetic algorithm is used to obtain the optimal solution of the model in the global task space of multi-robots cooperation systems. Finally, a Matlab-SimMechanics multi-robots simulation platform is developed to verify the correctness and practicability of results. The results of solution and simulation show that, the selected initial welding point and corresponding robots trajectory maximize the manipulability of multi-robots cooperative system subject to the constraint conditions.