This dissertation addresses Thrust Vector Control (TVC) design techniques for small launch vehicles with bounded roll rate. The first contribution of this dissertation is the development of a 6 Degree of Freedom (DoF) nonlinear model that serves as a tool for flight control system design. The nonlinear model is then trimmed and linearized, for a series of operating points, yielding a set of linear models. Building upon this result, decoupled lateral and longitudinal PID controllers are designed, as well as a Linear Quadratic Regulator (LQR) controller. The impact of flexible modes on the linear controller is assessed as well as the robustness of the LQR controller to parameter variations. Using the nonlinear model a backstepping controller is developed and implemented. Lyapunov stability analysis is used to assess the robustness and performance of this controller to different types of exogenous disturbances and model perturbations. Specific inaccuracies in the position of the center of mass lead to significant performance deterioration. Therefore an estimator is developed. The estimator design is integrated with the controller, thus stability of the overall system is ensured. Finally, a comparison between the performance of the proposed linear and nonlinear controllers is performed. The applicability of the nonlinear controller to other launch vehicles is discussed.