The lateral and upheaval buckling of subsea pipelines is investigated in this paper. For lateral buckling, analytical and numerical studies are conducted and compared and a new interpretation of localisation is given based on an isolated half-wavelength model. For upheaval buckling, a tabulated analytical solution based on a long heavy elastic beam resting on a rigid frictional foundation is given and the response under three types of localised initial imperfection is compared. A comparison of the lateral and upheaval responses of a subsea pipeline is made and indicates that excessive bending stress can be induced, particularly under upheaval buckling. The paper also highlights some differences between the current and previously published results.