The paper discusses load carrying capacity of steel cones subjected to combined loading by simultaneously acting uniform pressure and axial load. The following combinations of loads are considered: external/internal pressure plus axial tension. Depending on the load combination various modes of failure are studied. These includes bifurcation buckling, plastic load and plastic instability load.For the case of internal pressure/axial tension: envelopes of the first-yield, plastic load and plastic instability load are computed. All of these domains are convex and closed. This is not true for the case of external pressure and axial tension where bifurcation buckling becomes an active mode of failure.Due to substantial plastic straining, numerical results are based on true stress-strain modelling of material beyond necking and for up to fracture.