Abstract Analysis of idealised thin single-crystal wires under torsion based on the continuum theory of dislocations gives results in accordance with the critical thickness theory. The dislocation-free zone near the wire surface and the nearly-zero stress around the wire axis are predicted by both the continuum dislocation theory and critical thickness theory. It is demonstrated that the size effect at the onset of yielding, the distributions of stress and geometrically necessary dislocations in the thin wires in torsion, simply result from the critical thickness effect. A continuous increase of plastic strain from the neutral axis toward the wire surface is indicated. The plastic strain becomes (nearly) flat around the wire surface. Such a phenomenon is attributed to the fact that this is the region in which dislocations sources can operate, to provide the geometrically necessary dislocations required by the plastic strain gradient beneath. The results of continuum dislocation theory quantitatively elucidate the critical thickness phenomenon occurred in single-crystal wires under torsion. This links the continuum dislocation theory to the underlying physical picture of Matthews' critical thickness theory.