A proper buoyancy load formulation that complements the continuum formulation with incorporated beam theory in geometrically nonlinear analysis of flexible marine risers is presented. For continuous riser pipes, the hydrostatic pressure field only covers the circumferential surfaces thus hindering the buoyancy load approach. The present buoyancy load formulation is based on a vector calculus approach and essentially agrees with the well�known effective tension concept in the direct beam formulation. The gradient version of the divergence theorem (GVDT) is employed onto a continuous pipe segment subjected to circumferential hydrostatic pressure. The application of the GVDT results in the body force and cross�sectional surface traction which are regarded as the buoyancy load and boundary effect respectively. Emphasis is placed on the consequences of the boundary effect and the load definition of the buoyancy load in geometrically nonlinear analysis. The boundary effect occurs if either boundary end of the pipe system were uncapped. Further consequences of the boundary effect depends on the corresponding restraining locations and directions. Furthermore, the buoyancy load is ascertained to have weak nonlinearity hence the derivation of the augmented tangent stiffness matrix is deemed unnecessary. Finite element formulation of the corresponding external nodal load vectors is also presented using the isoparametric beam elements for discretization. © 2018 Elsevier Ltd