In this thesis, cable-suspended transportation system using unmanned aerial vehicle is studied. Using single or multiple rotor vehicle, slung-load flight has the advantage to place a cargo to the target spot without landing. However, the system has a risk that externally slung load can adversely affect and degrade the movement of a vehicle. Fluctuating motion of the payload and vehicle caused by heavier loads and shorter cable can be fatal. Mathematical modeling and control design for given system is conducted for rapid and robust stabilization of underslung payload. First, UAV slung-load system is designed using multi-pendulum, to describe the fluctuating motion of flexible cable. Dynamics of the system is derived with Euler-Lagrange Equations. Udwadia-Kalaba Equations (UKE) are also used to verify the equations. Linear model analysis has conducted to examine the characteristics of system in increasing the number of segments consisting cable configuration. Based on obtained results, linear and nonlinear control techniques are applied. Applied control techniques are linear PD control and adaptive control technique using artificial neural network. In PD control, added to the basic PD control technique, position error between the vehicle and payload are fed back for fast stabilization of payload. Improved performance of the method is shown by simulations. Finally, through the application of adaptive control technique using artificial neural network, robustness and rapid stabilization of payload is verified.