Engine control becomes increasingly important in newer cars. It is therefore interesting to investigate if a relatively new control method as Model Predictive Control (MPC) can be useful in engine control in the future. One of the advantages of MPC is that it can handle contraints explicitly. In this thesis basics on turbocharged engines and the underlying theory of MPC is presented. Based on a nonlinear mean value engine model, linearized at multiple operating points, we then implement both a linear and a nonlinearMPC strategy and highlight implementation issues. The implemented MPC controllers calculate optimal wastegate position in order to track a requested torque curve and still make sure that the constraints on turbocharger speed and minimum and maximum opening of the wastegate are fulfilled.