This thesis aims to provide insight into the conceptual design phase of Tetrahedron B.V. with regards to buckling stability. Currently, Tetrahedron B.V. assumes an effective length factor of one for determining the cross-section profiles of the Tetrahedron Crane. In this thesis, Euler-Bernoulli beams are used to model every member of this crane, where each element’s compressive force is related to the applied cargo load of the crane. The crane has various aspects to it that are assumed as ideal boundary conditions or partial restraints, some of these assumed boundary conditions are then modelled by partial restraints to see its effect on the critical buckling load. The critical buckling load of Euler-Bernoulli beams, also known as the linear bifurcation point, is found by solving the eigenvalue problem, which results in the load under which the system fails from buckling instability. The current crane, the version zero design, was assessed. The buckling model created in this thesis is verified through limit cases of simplified models and the results from a FEM software, whilst always remaining critical to all comparisons. This crane design is deemed to be stable from buckling failure within the intended safe working load of the crane. With this crane design, using an effective length factor of one in the conceptual design phase is suitable. However, the Tetrahedron crane design has changed quite dramatically since this thesis began, so the thesis also adapted to understand and analyse the general trends that appear when key structural or geometrical inputs change. This is done through a sensitivity analysis where the critical buckling load is determined for a variety of geometrical and section properties to see at how the critical load changes given input changes. This uncovered some changes in the critical buckling load and eigenmode of the crane given certain conditions. Most significantly, a sharp decrease in critical buckling load when the crane heel girder’s (which is one of the members) is greater than eleven meters. This decrease in critical buckling load would in fact mean that the crane would fail from buckling instability within its safe working load and means that the effective length factor is not related to the shape of the crane itself. As there are so many geometrical and structural parameters in the crane, not all of them could be assessed in the sensitivity analysis. But ultimately, the model in this thesis, programmed in MATLAB, can be used by Tetrahedron B.V. for future iterations to the crane in the conceptual design phase.