This is a Ph.D. dissertation. The response of aircraft to stochastic atmospheric turbulence plays an important role in, for example, aircraft design (load calculations) and flight simulation (handling qualities research and pilot training). In order to simulate these aircraft responses, an accurate mathematical model is required. Two classical models will be discussed in this thesis that is the Delft University of Technology (DUT) model and the Four Point Aircraft (FPA) model. Although they are well established, their fidelity remains obscure. The cause lies in one of the requirements for system identification; it has always been necessary to relate inputs to outputs to determine, or identify, system dynamic characteristics. From experiments, using both the measured input and the measured output, a mathematical model of any system can be obtained.