We study the minimum time control problem of the launchers. The optimal trajectories of the problem may contain singular arcs, and thus chattering arcs. The motion of the launcher is described by its attitude kinematics and dynamics and also by its trajectory dynamics. Based on the nature of the system, we implement an efficient indirect numerical method, combined with numerical continuation, to compute numerically the optimal solutions of the problem. Numerical experiments show the efficiency and the robustness of the proposed method.