The normal contact of a frictionless elastic coated cylinder indented by a flat rigid surface is solved using a Michell–Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. The boundary conditions are chosen such that the elastic layer rests on the cylindrical substrate. When the contact region is small compared to the radius of curvature of the coated cylinder, semi-analytical solutions are obtained by exploiting dual series equation techniques. The stresses on the surface are evaluated for plane strain. The results may have application to coated cylindrical structures, bimaterial inclusions, or pin-joint contact.