A probabilistic stability analysis of an embankment dam taking into account soil spatial variabilities is presented in this paper. The effective cohesion and friction angle of the backfill are modelled as two anisotropic cross-correlated lognormal random fields by using the Karhunen–Loève Expansion. The probabilistic analyses are performed by a meta-modelling technique SPCE/GSA which combines the Sparse Polynomial Chaos Expansion (SPCE) and the Global Sensitivity Analysis (GSA). This technique is targeted to deal with high dimensional stochastic problems and can provide a variety of interesting results in terms of probability density function (PDF) and statistical moments of the model response, failure probability and sensitivity index of each input variable. Concerning the deterministic calculations, two models (limit equilibrium and finite difference) are created and compared in a probabilistic framework. The influences of the soil spatial variability and the cross-correlation between the shear strength parameters on the reliability analysis results are investigated.