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The dispersion relations and modes for a dielectric-filled rectangular waveguide with transverse slots are investigated. The differences between the air-filled and the dielectric-filled rectangular waveguides with transverse slots are analyzed. The dielectric-filled rectangular waveguide with transverse slots supports a leaky waveguide mode, a surface-wave mode and a proper waveguide mode. The complex propagation wavenumber is calculated by enforcing an aperture magnetic field integral equation using either a space-domain approach or a spectral-domain approach. The physical significance of the solutions is explained. The theoretical results agree very well with the results from HFSS simulation.