Thermal loads in submarine pipelines generate an axial compressive load that can force the pipeline to buckle, leading to failure if these loads are not considered in the design. Buried pipes are constraint to displacements in all directions, which leads to a high compressive load in the longitudinal axis and makes the pipes more vulnerable to buckling. If buried pipes under thermal loads do not buckle, a high-stresses state takes place when it is combined with high-pressure conditions. In this work, a simple mechanical model to determine the axial buckling load of a buried pipeline is proposed. The model is based on a simply supported beam subjected to a distributed transverse load representing the soil uplift resistance obtained from a referenced model, and an axial compressive load that represents the effective axial force and is computed according to the DNV-RP-F110. Additionally, the pipe–soil system is analyzed through a non-linear finite element model to compare the results with the analytical solution. The proposed simple mechanical model can capture the upheaval buckling behavior and provides results that are consistent with the numerical analysis, specifically for the two main parameters evaluated, namely, the initial pipe curvature and the magnitude of the transverse load.