This paper proposes a two-dimensional axisymmetric numerical modelling of an earth platform over a clayey sand improved by stiff vertical piles using a finite-difference continuum approach. The study focuses on the surface settlements and the stress efficacy of the improvement system. Only the soil parameters are considered as random variables and two assumptions (normal distribution or non-normal distribution) are used. The first-order reliability method (FORM) is applied to calculate the reliability index. Response surface methodology (RSM) allows for access to the Hasofer-Lind reliability index and is optimized by the use of a genetic algorithm. The Hasofer-Lind reliability index is calculated for two distinct cases. Firstly, only the geomechanical parameters of the clayey sand are considered as random variables; secondly, the parameters of both the clayey sand and the earth platform are considered. The results show that the reliability of a single soil layer is safer than the reliability of the whole system.