The instability of beam-columns with crossarms and externally prestressed cable stays is studied analytically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. Three principal zones of behaviour are identified with two of these each having two sub-zones that relate the critical buckling load to the initial prestressing force applied to the stay cables. The ultimate load-carrying capacity of the beam-columns is evaluated by conducting nonlinear finite element analysis within the commercial package ABAQUS. Results show that the analytically derived critical buckling loads generally provide safe predictions of the ultimate loads due to significant post-buckling strength. It is found that releasing the geometric double symmetry of the system can make for a significantly more efficient structure due to the effect of pre-cambering against the self-weight. The strength and efficiency of stayed beam-column systems opens up a range of potential applications, including lighter alternatives to conventional props to support wide excavations, which currently utilize very heavy steelwork.