Offshore pipelines are commonly installed empty in order to reduce the installation tension due to the weight of the suspended section (see Chapter 2). In addition, during operation they are periodically depressurized for maintenance. Thus, external pressure is an important load parameter in design; indeed, it is often the prime parameter. This chapter deals with the mechanics of buckling and collapse of long pipes under external pressure. Thinner pipes used in shallower waters buckle elastically, but collapse due to postbuckling inelastic action. The classical elastic buckling pressure is derived in Section 4.1, followed by the derivation of Timoshenko's design formula for the onset of collapse of an initially ovalized pipe. Thicker pipes used in deeper waters buckle and collapse in the plastic range. In Section 4.2, plastic buckling equations are derived. Their relative simplicity makes them useful tools in design. Practical factors that affect collapse include initial imperfections such as ovality and wall thickness variations. Other factors include residual stresses, yield anisotropy, etc. The influence of such factors is best treated numerically. Section 4.3 presents the external pressure part of the formulation and solution procedure of the custom computer code BEPTICO [4.1], capable of including these aspects of the problem. Section 4.4 presents a parametric study of buckling and collapse of elastic-plastic pipe under external pressure. Section 4.5 outlines how actual pipe imperfections can be measured. Examples of typical shape and wall thickness imperfections in seamless pipes are presented and used in collapse calculations.