This paper presents a possible framework for dealing with uncertainties in geotechnical engineering based on more recently introduced mathematical theories. Random sets are employed to describe the variability of material parameters and geometrical data. After a brief introduction of the basics of the proposed approach application to boundary value problems are presented. First a simple slope stability analysis is performed where emphasis is put on the comparison with a more rigorous method combining finite element modelling with stochastic modelling of soil behaviour, namely with random field theory. The purpose of this comparison is mainly to show that the approximation introduced for taking into account spatial variability is acceptable within certain limits for use in practical applications. Finally, results obtained for a practical example will be discussed. Here, comparison with in situ measurements are provided for a deep excavation problem and it is shown that the calculated most likely range of displacements compares well with measurements. Furthermore, an assessment of the probability of damage of a building, situated adjacent to the excavation, is in line with observed behaviour.