On-bottom pipelines for transporting oil and gas in deep water undergo significant changes in temperature and pressure during operating cycles, which cause a tendency for lateral buckling. Prediction and control of this phenomenon are required for the safe design and operation of these pipelines. However, the soil response under combined vertical and lateral loading is a significant area of uncertainty, and current practice relies on empirical expressions for the estimation of lateral pipe-soil resistance. This paper reports the results of finite element (FE) analyses of shallowly embedded pipelines under vertical and horizontal load. These analyses have been compared with collapse loads calculated using the upper-bound theorem of plasticity, and are used to construct yield envelopes defining the limiting combinations of vertical and horizontal load. The FE limiting loads were found to compare well with upper-bound plasticity solutions, and the internal soil displacements calculated in the FE analyses match the upper-bound and experimentally observed deformation patterns. The yield envelopes generated by the FE and upper-bound analyses have been fitted by simple solutions, which aid assessment of the ultimate resistance of shallowly embedded pipelines.