The design of controlled suspensions systems for road vehicles aims to optimize the performance of the vehicle with regard to comfort and road handling. Vehicle suspensions serve several conflicting purposes. The goal of this paper is to introduce the design and analysis of a control strategy, for semiactive suspensions in road vehicles, based on model predictive control (MPC) strategies, and to compare its performances with well established semiactive control algorithms such as "On-Off Sky-Hook" and "clipped" strategy. The investigation of the properties of the proposed control strategy has been carried out by means of simulation results on a quarter car model involving "benchmark" road profiles employed in industrial tests.