The three-dimension motion of a parachute and payload system is studied. Both the parachute and payload are assumed to have six degrees of freedom. They are coupled by a riser. The nonlinear differential equations of motion for a parachute-payload system are developed, which model the parachute suspension lines and the riser as inelastic elements. The resulting math model is then applied to analyze the dynamic performance of a drogue parachute recovery system. The simulation results are presented.