Many aircraft need to have ability to accomplish given missions stably and effectively. Modern complex aircraft missions have to also be achieved by pilots’ simple compensation control of aircraft and pilots’ load to complete given missions needs to be decreased while aircraft carry out their missions. Therefore, it is important to design aircraft control systems to satisfy requirements of flying and handling qualities which are criteria showing how aircraft response is easy, predictable and effective about pilots’ command for performing a flight mission. Furthermore, robust and good performance control systems which meet the criteria must be designed because most high-performance commercial and military aircraft do not guarantee the flying and handling qualities of the vehicles or actually unstable. The objective of this paper is to analyze and understand specifications for flying and handling qualities of longitudinal and lateral-directional aircraft motions which are described in MIL-STD-1797A. Moreover, the 6-DOF nonlinear equations of motion and linear model of F-16 fighter are developed and the aircraft control systems by using dynamic inversion synthesis are designed to satisfy the flying and handling specifications. Dynamic inversion is used since aircraft control systems which have desired response characteristics can be easily designed with this synthesis. The numerical simulations are performed to investigate the performance of the designed control systems according to low-order equivalent systems, bandwidth criteria, Neal-Smith criteria and Gibson\`s dropback criteria, etc.