This paper addresses the guided-wave propagation in an
open uniaxial ridge waveguide. The analysis is focused on the discrete modes, although including both guidance and leakage behavior. It is shown that, beyond a certain critical frequency, the surface guided modes may turn into leaky modes, due to the TE-TM mode coupling at the waveguide lateral boundaries. The numerical results were obtained using a conventional mode matching technique with a finite number of surface waves in each region. The results obtained for the guided modes are validated by comparison with those obtained through a more accurate analysis. The influence of the anisotropy and the geometrical parameters on the attenuation and phase constants of the leaky modes is shown.