Dealing with uncertainty, caused e.g. by material parameters varying in a wide range or simply by a lack of knowledge, is one of the important issues in geotechnical analyses. The advantages of numerical modelling have been appreciated by practitioners, in particular when displacements and deformations of complex underground structures have to be predicted. Therefore, it seems to be logical to combine numerical modelling with concepts for the mathematical representation of uncertainties. Recent theoretical developments and advances made in computational modelling have established various methods which may serve as a basis for a more formal consideration of uncertainties as has been done so far. Random set theory offers one of these possibilities for the mathematical representation of uncertainties. It can be viewed as a generalisation of probability theory and interval analysis. After a brief introduction of the basics of the proposed approach an application to a boundary value problem is presented. The results show that the assessment of the probability of damage of a building, situated adjacent to the excavation, is in line with observed behaviour.