The optimization-based dynamic prediction of 3D human running motion is studied in this paper. A predictive dynamics method is used to formulate the running problem, and normal running is formulated as a symmetric and cyclic motion. Recursive Lagrangian dynamics with analytical gradients for all the constraints and objective function are incorporated in the optimization process. The dynamic effort is used as the performance measure, and the impulse at the foot strike is also included in the performance measure. The joint angle profiles and joint torque profiles are calculated for the full-body human model, and the ground reaction force (GRF) is determined. Several cause-and-effect cases are studied, and the formulation for upper-body yawing motion is proposed and simulated. Simulation results from this methodology show good correlation with experimental data obtained from human subjects and the existing literature.