Single-mode propagation conditions of X-ray waveguides are investigated by numerical calculations in order to understand the importance of waveguide design parameters, such as core thickness and the optical constants of waveguide materials, on the transmission and coherence properties of the waveguide. The simulation code for mode analyzing is developed based on a numerical solution of the parabolic wave equation. The initial boundary value problem is solved numerically using a finite-difference scheme based on the Crank-Nicolson scheme. The E-field intensities in a core layer are calculated at an X-ray energy of 8.0 keV for air and beryllium(Be) core waveguides with different cladding layers such as Pt, Au, W, Ni and Si to determine the dependence on waveguide materials. The highest E-field intensity radiated at the exit of the waveguide is obtained from the Pt cladded beryllium core with a thickness of 20 nm. However, the intensity from the air core waveguide with Pt cladding reaches 64% of the Be-Pt waveguide. The dependence on the core thickness, which is the major parameter used to generate a single mode in the waveguide, is investigated for the air-Pt, and Be-Pt waveguides at an X-ray energy of 8.0 keV. The mode profiles at the exit are shown for the single mode at a thickness of up to 20 nm for the air-Pt and the Be-Pt waveguides.