This paper studies the stability of a system consisting of a drone with a heavy payload through both linear stability analysis and nonlinear simulations. The stability is studied with respect to two payload parameters: the length of the arm the payload is suspended from and the mass of the payload. Linearizing the drone-payload system around vertical flight results in a linearized system that is marginally stable with five negative, real eigenvalues and seven zero-eigenvalues. The presence of seven zero-eigenvalues makes it difficult to predict the stability of the nonlinear system so nonlinear simulations are completed to understand how the drone-payload system reacts to external disturbances. To directly study the severity of the nonlinear system’s instability, the system is subjected to an initial, one-second wind disturbance that induces different initial conditions on the system. The results of the nonlinear simulations indicate that the presence of a suspended payload will always cause the drone-payload system to be unstable. Both an increase in the length of the payload arm and the payload mass will individually increase the deviation of the system from the expected path.