Geotechnical materials exhibit significant heterogeneity in their spatial distribution due to the combined effects of sedimentation processes, geological history, and environmental factors. Traditional design methods for horizontally loaded piles assume that soil parameters are spatially homogeneous constants and use idealized calculation models for analysis, which often leads to an overestimation or underestimation of the horizontal bearing capacity of pile foundations. This study employs the stochastic finite element method and selects the internal friction angle of sandy soil as a key variable parameter. It systematically investigates the influence mechanisms of the spatial variability coefficient of sandy soil, horizontal and vertical correlation distances on the horizontal bearing characteristics and failure probability of flexible single piles. The results show that the spatial variability of the internal friction angle of sandy soil significantly affects the horizontal bearing performance of the pile foundation: as the variability coefficient of the internal friction angle and the vertical correlation length increase, the mean horizontal ultimate bearing capacity decreases, while the coefficient of variation of the bearing capacity increases. This indicates that the spatial variability of the soil not only reduces the average bearing capacity but also increases the dispersion of the bearing capacity. Further analysis of seven typical variability combinations reveals that the failure probability of flexible single piles generally exceeds 50%. Based on these findings, this study innovatively establishes an explicit functional relationship between the safety factor and failure probability, providing a theoretical foundation and practical tool for the reliability design of horizontally loaded piles.