Abstract This study provides a probabilistic procedure for analysing the stability of massive bridge abutments. The procedure is based on simulation techniques. To analyse the stability a model is applied which considers five cases of losing the equilibrium. To describe the random variability of soil properties, polygonal probability distributions are proposed, which are especially useful in sumulation calculations. Examples of description of some soil parameters by polygonal distributions together with verification by statistical testing are presented. The proposed method is examined in numerical examples and applied to the analysis of the influence of individual parameters on the probability of loss stability. The problem of the accuracy of calculations is also discussed. Numerical examples show the usefulness of the presented methodology. The randomness of the friction angle of the geotechnical layer directly under the base of an abutment is shown to have the greatest effect on the probabilistic characteristics of the stability. The probability distribution of the stability measures in the case of exceeding the bearing capacity may differ significantly from the normal distribution.