We consider an extreme type-II superconducting wire with non-smooth
cross section, i.e., with one or more corners at the boundary, in the
framework of the Ginzburg-Landau theory. We prove the existence of an
interval of values of the applied field, where superconductivity is
spread uniformly along the boundary of the sample.
More precisely the energy is not affected to leading order by the
presence of corners and the modulus of the Ginzburg-Landau minimizer
is approximately constant along the transversal direction. The
critical fields delimiting this surface superconductivity regime
coincide with the ones in absence of boundary singularities.