The relative structural stability of the transition metals and their alloys for a tetragonal deformation is investigated. Total energy calculations demonstrate that the nonequilibrium cubic structures are [ital locally] [ital unstable] with respect to this deformation mode at low temperatures, i.e., the cubic elastic constants ([ital c][sub 11][minus][ital c][sub 12]) are negative. Thus, these phases are not appropriate reference states for alloy phase diagram constructs and if such phases do occur at high temperature, the local stability must be due in large part to entropy contributions to the free energy.