##### Abstract

In anisotropic superconductors having an arbitrary orientation of the sample surface relative to the crystal principal axes, the surface critical field H-c3 is less than 1.695H(c2) unless the field is situated along one of the principal crystal planes. Below H-c3 in the vicinity of nucleation, the order parameter scales as rootH(c3)-H. Computational studies for infinite cylinders having rectangular cross sections are presented which show that, due to corners and a finite cross section, the surface superconductivity state persists for fields above the theoretically predicted value for semi-infinite samples. They also show that vortices exist within the Surface superconductivity sheath above the bulk critical field.