This paper presents a comprehensive study on the effect of spatial variability of the elastic modulus on vertical stress distribution in an elastic half-space due to strip loading. The modulus of elasticity is considered as a random variable which follows a log-normal probability distribution. A random field theory based on a Cholesky decomposition technique is used to generate a two-dimensional random field in the elastic half-space. Monte Carlo simulation is performed to generate various random fields with spatially varying elastic modulus. A two-dimensional random finite-element model is developed for a strip loading on an elastic half-space by coupling the random fields generated by Monte Carlo simulation with finite-element analysis. A detailed investigation of the effect of statistical variables defining spatial random variation of the elastic modulus on the vertical stress distribution and the settlement analysis in random elastic half-space is performed. The present study indicates that the spatial random variation of elastic modulus of the soil has a significant effect on the vertical stress distribution and the settlement analysis in the elastic half-space. © 2022 American Society of Civil Engineers.