This paper deals with the mathematical model of dynamic behaviour of a beam resting on viscoelastic random foundation for which the modulus of subgrade reaction is assumed to be a homogeneous random function of the space variable. An approximate analytical solution for the fourth-order differential equation with random parameters is obtained in the case of a ∞ C -class correlation function. This higher order regularity of correlation function implies the regularity of associated stochastic function  in the sense of the mean-square analysis . The numerical results for the average displacement have been obtained by using Bourret’s approximation method. A special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in the numerical examples.