The penetration resistance and the force required to cause lateral movement of pipelines at shallow embedment in soft sediments has received increasing attention in recent years, as deep-water oil and gas reserves are developed. In deep water, pipelines are generally laid untrenched on the seabed, but embed by a small amount owing to their own weight and the additional loads imposed during the laying process. Pipeline design requires the possibility of lateral buckling during temperature-induced expansion to be considered, and the soil restraint at different combinations of vertical load and pipeline embedment is critical for such design (Bruton et al., 2006).This note documents yield envelopes derived from upper-bound plasticity solutions for pipelines embedded by up to half a diameter in clay soils with either homogeneous shear strength or shear strength increasing proportionally with depth. The pipeline is assumed to ‘break away’ at its trailing edge, a feature of behaviour that is consistent with experiments, where only transient negative excess pore pressure is maintained on the trailing edge. The solutions are placed in context, and compared with finite element solutions and experimental data in a separate paper (Merifield et al., 2008).At this stage, the effect of the self-weight of the soil has been ignored, largely because it has little effect on the pipe resistance at shallow embedment for practical ratios of effective stress to shear strength. The solutions may be extended to allow for self-weight relatively simply.