The shock compression of the preexisting southward directed magnetic field can enhance a geomagnetic disturbance. A simple theoretical model is proposed to study the geoeffectiveness of a shock overtaking a preceding magnetic cloud. Our aim is to answer theoretically the question how deep the shock enters into the cloud when the event just reaches the maximum geoeffectiveness. The results suggest that the minimum value of Dst* decreases initially, then increases again while the shock propagates from the border to the center of the cloud. There is a position where the shock compression of the preceding cloud obtains the maximum geoeffectiveness. In different situations, the position is different. The higher the overtaking shock speed is, the deeper is this position, and the smaller is the corresponding Dst∗min. Some shortcomings of this theoretical model are also discussed.