This paper outlines a method for the probabilistic modelling of residual stress in the advanced analysis of steel structures. An extensive survey of literature on a large number of experimental measurements of residual stress in hot-rolled I-sections is presented. An error minimization is then performed to obtain appropriate scale factors to apply to common residual stress patterns to obtain the best agreement with available experimental data. The statistical distributions of the scale factors are derived. Frames with deterministic and random residual stresses are then analysed by advanced geometric and material nonlinear analysis using the proposed scale factors to determine the influence of residual stress and its different patterns on the ultimate strength and reliability of steel frames. It is shown that the strength of steel frames comprising columns with a range of slenderness values is generally much less influenced by residual stress than individual columns.