We use the local density approximation to density functional theory to re-examine the well-known ‘theoretical strength’ of metals. This is done by calculating ideal twin stress in five b.c.c. transition metals, and in Ir, Cu and Al. This leads us to a first-principles, quantum-mechanical confirmation of the Frenkel model in the theory of plasticity which has previously been thought to have been too oversimplified to be realistic. We discuss this result in the light of the Peierls—Nabarro model and relate it to the deformation behaviour of group-5 and group-6 transition metals. We also include a general analysis of the geometry of the problem that can be readily extended into a number of new areas in the theory of phase transformations.