Bending in the presence of external pressure is experienced by pipelines during their installation and also subsequently during their operation. In installation methods such as S-lay (Figure 2.15), J-lay (Figure 2.19), and reeling (Figure 2.4), the pipe is bent under relatively high external pressure in the sagbend [9.1, 9.2]. The pipeline is also bent under external pressure as it conforms to surface undulations on the seafloor. Bending at the sea floor can also be experienced due to snaking resulting from pipe expansion caused by the passage of hot hydrocarbons (in some cases purposely induced, in others accidentally). It is also a condition that can develop in case of upheaval buckling of a section of a buried pipe. Bending ovalizes the pipe cross section, which of course reduces its resistance to external pressure. This interaction through ovalization is aggravated by inelastic material effects, which usually come into play in lower D/t pipes used for offshore applications. This chapter deals with the mechanics of inelastic bending in the presence of external pressure and the associated limit states. The development of this interaction starts with the behavior under pure bending and pure external pressure. The reader would benefit from exposure to Chapters 4 and 8 before embarking on the following material.