This paper extends the use of the skew boundary condition in two- and three-dimensional (3D) finite element analysis for both structural and geotechnical applications when the need of the freedom directions at the interface nodes is different from the global Cartesian directions. For instance, jack-up structures have three conical-shaped footings, whose freedom directions at the interface nodes are not suitable for Cartesian directions. In addition, there is no axisymmetric movement of the soil as the load is applied to the jack-up's hull. Thus, a more reliable solution of jack-up-soil interaction should be analyzed in a full 3D version. This paper develops a simple 3D interface model for soil-structure interaction that uses skew boundary conditions and incorporates the visco-plastic strain method into the finite element program. The work was validated by computing bearing capacity factors of conical footings with different scenarios, such as plane strain, axisymmetric and 3D analysis. The results of the present analysis are in good agreement with the existing solutions. The fields of the displacement vector and failure patterns at the collapse state are demonstrated and discussed for each apex angle, and the influence of the conical angle on the bearing capacity factor (Nc) is also examined. © 2021 Elsevier Ltd