A full vector H field finite element formulation has been developed for the analysis of a wide range of uniform guided wave problems. It deals with microwave or optical structures where the permittivity has arbitrary variation in the transverse cross section. The permittivity can have a tensor of arbitrary anisotropy, limited only to being loss-free. Infinite elements have been introduced to represent well the fields in an open type of waveguide. A matrix algorithm is used which takes complete advantage of the matrices' sparsity. Computed results are illustrated with optical channel and rib guide, image guide, and waveguide containing a skew uniaxial dielectric.