The classical problem of a beam on an elastic foundation (BOEF) has long been of practical interest to geotechnical engineers, because it provides a framework for computing deflections, not only of foundations, but also of vertically oriented laterally loaded piles. The supporting soil can be modeled as an elastic medium which can be calibrated to represent the stiffness of the soils adjacent to the beam (or pile). In this study the influence of spatially random soil stiffness on deformations of transversely loaded homogeneous piles and beams is investigated. The approach involves a combination of finite element analysis, random field theory and Monte-Carlo simulations. Following code validation, the objective is to quantify the influence of statistically defined soil stiffness (mean, standard deviation and spatial correlation length) on the mean and standard deviation of pile or beam deflection. This leads naturally to a probabilistic interpretation in which the probability of deflections exceeding some design threshold can be quantified.