In this paper formulae are derived for the surface wave of the elliptic cylinder. The mode described is an E-mode that possesses the evanescent structure in the transverse plane of the cylinder. The elliptic surface wave is shown to be similar in some respects to the surface wave associated with single wire transmission lines of circular symmetry to which form the elliptic surface wave degenerates when the eccentricity of the ellipse tends to zero. In a separate section a slightly deformed circular guide is discussed in detail and it is shown that the performance of a circular guide is substantially unaffected by slight deformation of its geometry. The last section of the paper deals with different types of elliptic guides that are likely to be encountered. The elliptic dielectric rod waveguide and a corrugated elliptical guide are typical examples, while the homogeneous metal guide and the dielectric coated perfectly conducting elliptical rod are analysed in detail.