A reliable design of geotechnical structures requires an appropriate estimation and consideration of the parameter's uncertainties. Traditional design codes account for the uncertainties by using conservative factors. This paper presents a reliability-based analysis of the seismic internal stability of geosynthetic reinforced earth retaining walls. The deterministic computation of the structure safety factor is based on the upper bound theorem of limit analysis. The discretization technique is used to generate the rotational failure mechanism so that the seismic loading can be implemented by the pseudo-dynamic approach. The considered uncertainties involve the soil shear strength parameters, seismic loading and reinforcement strength parameters. The Sparse Polynomial Chaos Expansion combined with Monte Carlo Simulation is the reliability method considered to carry out the probabilistic analysis. The influence of the correlation between the soil parameters and the random variables distribution type on the probabilistic results are investigated and discussed. A global sensitivity analysis is performed in order to specify the contribution of each random variable to the reinforced earth retaining wall safety factor.