Advanced driving assistance systems (ADAS) are one of the latest automotive technologies for improving vehicle safety. An efficient method to ensure vehicle safety is to limit vehicle states always within a predefined stability region. Hence, this thesis aims at designing a model predictive control (MPC) with non-overshooting constraints that always confine vehicle states in a predefined lateral stability region. To consider the feasibility and stability of MPC, terminal cost and constraints are investigated to guarantee the stability and recursive feasibility of the proposed non-overshooting MPC. The proposed non-overshooting MPC is first verified by using numerical examples of linear and nonlinear systems. Finally, the non-overshooting MPC is applied to guarantee vehicle lateral stability based on a nonlinear vehicle model for a cornering maneuver. The simulation results are presented and discussed through co-simulation of CarSim® and MATLAB/Simulink.