Single mode propagation in three-layer step index elliptical fiber waveguides is investigated theoretically. Previous analysis of the elliptical dielectric tube waveguide is extended to include cladded, W-type and tube-type fibers. Numerical results on cutoff characteristics of the first higher-order mode and phase coefficient, group velocity and power distribution characteristics of the dominant modes are presented over a wide range of parameters. A two-layer step index elliptical fiber waveguide is presented as a special case. High eccentricity single mode fibers have small modal beat lengths but have small core size and greater power distribution in the claddings. W-type fiber in the middle range of eccentricities is suggested for single mode single polarization applications.