The analysis of the random behavior of beams on an elastic foundation, considering a two-dimensional random elastic modulus, contributes to bringing the analytical model closer to the physical model of the problem and enhancing the reliability of structural calculations. This paper aims to develop a Monte Carlo simulation (MCs) to represent the two-dimensional random field of elastic modulus combined with the finite element method to analyze the random response of beams resting on an elastic foundation according to the Winkler model. The spectral representation method generates the two-dimensional elastic modulus\u27s Gaussian. This sample function is used to construct the formulation of finite elements. The influence of the random field\u27s standard deviation, the correlation distance along the in-plane axes, and the stiffness of the elastic foundation on the coefficient of variation of displacement are also investigated and analyzed in detail in this article. The two-dimensional randomness of the elastic modulus and the stiffness coefficient of the foundation significantly affect the random response of the beam. The coefficient of variation (COV) of displacement tends to increase when the standard deviation of the stochastic field or the correlation distance along the axes increases. Still, conversely, when the stiffness of the elastic foundation rises, the coefficient of variation decreases. The COV of displacement approaches the standard deviation value of the stochastic field of material properties when the correlation distance along the axes approaches infinity
