Abstract The mean-square bending moment of a thick rectangular plate excited by a uniform distribution of stationary random forces that are uncorrelated in space is calculated. The plate has in-plane compressive or tensile stresses. In addition, the plate is mounted on an elastic foundation. Numerical results are given for plates with uniform initial stress when the temporal correlation function of the excitation possesses an exponential decay. In general it can be said that the position on the plate where the mean-square moment takes on a maximum value depends upon the relative values of the initial stress, the stiffness of the foundation and the aspect ratio of the plate. The mean-square response amplitude of the plate on a foundation never exceeds that of the plate without a foundation, regardless of the intensity of the initial stress or the geometrical configuration of the plate.