Diffraction and refraction phenomena at the entrance of a hollow x-ray waveguide with weakly absorbing dielectric cladding layers are investigated using two independent approaches: (a) analytical and (b) numerical solutions of the wave equation in the paraxial (parabolic) approximation. It is shown that the wave penetrating through the cladding material substantially modifies the wave field near the waveguide entrance. It results in a significant increase of the total energy flux inside the guiding layer and in additional spatial modulation of the electromagnetic field.