Thrust Vector Control (TVC) is one means of controlling air vehicles to follow a desired flight path where, in particular, those that are flexure jointed are currently the most commonly used. Often, dynamic modeling of such systems is for the case where a universal gimbal joint is present, which neglects uncertainties in the dynamics, such as vertical motion of the pivot point of nozzle and misalignment. This paper gives early results on a new approach to dynamic modeling of TVC systems that includes one more degree of freedom compared to previously reported models and also enables the flexure jointed structure to move along vertical direction on the flight axis. A Computed Torque Control Law (CTCL) is then designed for the new resulting model with the potential for higher tracking accuracy and lower feedback gains. A simulation based case study is given to demonstrate the new design.