ESDU 83034 provides data for isotropic cylinders subjected to either axial load or combined axial load and internal pressure. The data relate to cylinders of uniform wall thickness. A correction for the reduction in the buckling stress resulting from initial irregularities is provided. This correction has been used to analyse the results of 60 compression tests taken from the literature to determine the initial irregularity value implied. The results of a statistical analysis of the implied values is also presented. This allows use of the correction for the effect of initial irregularities in design with any desired probability and attached confidence level. Also presented is the analysis of the increase in buckling stress associated with increased internal pressure. This has been determined by applying the correction for initial irregularities to over 150 test results. Mean and limit curves through the resulting analysis are provided. A practical worked example illustrates the use of the data.