The need for reliability based design (RBD) has increased over the years, due to the necessity for more complex and efficient designs. The uncertainty, which must be accounted for during RBD, can be divided into two categories; namely, aleatoric uncertainty and epistemic uncertainty. A stochastic analysis is required to take account of both the natural variability and epistemic uncertainty. The random finite element method (RFEM) uses random fields, i.e. property fields generated from the measured statistics, for modelling the natural (spatial) variability of soil properties, within a finite element framework. Random material point method (RMPM) is comparable with RFEM, in that it combines random field theory with a numerical simulation method. RMPM can be used to model any problem involving large deformation under the influence of spatial variability. Cone penetration tests (CPTs) are typically a good candidate for the quantification of spatial variability where a ’real’ soil is shown with CPT measurements superimposed.