A dielectric waveguide structure using rectangular dielectic strip is analyzed directly in terms of the wave equation for quasi TE and quasi TE and quasiTM modes. This problem can be solved, with no approximation in the wave equation for the electric field $vec{E}$ and magnetic field $vec{H}$ inside and outside the dielectric rectangular waveguide matching the boundary conditions between interfaces. This leads to an eigenvalue problem where spurious modes do not appear. Dispersion characeristic examples are presented for square and rectangular waveguides. The formulation is general and can be used for compuarison with ogher methods such as FDM or FEM in various structures.