¡n this paper, analytical solutions are derived for the case when an elastic water-backed plate (WBP) is subject to an exponential shock loading near a fixed solid boundary. Two cases, a rigid plate and an elastic plate represented by two mass elements connected by a spring and a dashpot, are studied. The analytical solution is extended The results show that the pressure responses at the front and back surfaces of the plate are gr'eatly affected by the proximity to the fixed boundary, the fluid-structure interaction parameter, the ratio of the shock decay time to the natural period of the structure, and the rise time of incident pressure. The effect of structural damping (assuming a typical material damping coefficient of 5%) is found to be practically negligible compared to the other four parameters.