In the present paper, the structural capacity of relatively thick inelastic steel cylindrical tubes under external or internal pressure and concentrated radial loads is investigated, through a rigorous finite element analysis, as well as using a simplified analytical model. For zero pressure, the tubes exhibit inelastic cross-sectional deformation and are capable of dissipating a significant amount of plastic energy. The energy absorption capacity, as well as the ultimate transverse load, are reduced in the presence of external pressure. The effects of internal pressure are also examined. Results are reported in the form of load-deflection curves for different pressure levels. In addition, collapse envelops showing the interaction of pressure versus radial transverse loads are presented. The conclusions of this study are important for the structural integrity of cylindrical steel tubulars for pipeline and other offshore applications.