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Application of the method of moments (MoM) with eigenmode expansion to a waveguide slot array enables fast analysis even though the number of the slots is large because of small analysis scale, that is, the unknowns are sources placed only in the slot apertures. However, the method is applicable typically to slot shapes whose eigenmodes are analytically derivable. The hybrid MoM/FEM was proposed for analysis of an array of slots with arbitrary shapes. The eigenmodes of a waveguide with the cross section of the slot shape are numerically derived by the finite element method (FEM) for the basis functions of the magnetic currents in the slot in MoM. In this paper, we apply the hybrid MoM/FEM to an X-shaped cavity-backed wide slot 2×2-element sub-array in the corporate-feed double-layer hollow-waveguide slot array antenna. The 2×2-element sub-array is the radiation unit and fed in equal amplitude and phase by a coupling slot placed at each end of the feed waveguide in the antenna.