For economical and ecological reasons aircraft are required to become more efficient by reducing fuel consumption and CO$_2$ emissions. One way to achieve these objectives is to decrease the weight of the aircraft structure. The reduction is, however, limited by the structural requirement that the aircraft must be able to withstand the forces and stress induced by maneuvers, turbulence, and gusts. Reduction of the forces and stress, for example by suitable flight control schemes, allows lighter structures and thus more efficiency. In this paper we focus on the problem of alleviating gust loads at critical locations of the airframe. This is accomplished via a model predictive control approach that accounts for look ahead measurements of incoming gust disturbances via light detection and ranging (LIDAR) systems. Deflecting control surfaces are used by the predictive controller to reduce the load effects caused by the disturbance, the aircraft rigid body, and the structural response. The proposed controller design takes actuator deflection- and rate-limitations, the complex multiple-inputs multiple-outputs system structure, and the objective to reduce critical loads directly into account. Predictive control proved itself to be an effective control strategy for gust load alleviation.