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In this study, we discuss the multiplet structure observed in the Cu 2p- and 3p-XPS in La₂CuO₄, CuO and Cu dihalides using the single-site Anderson model. We take into account the multiplet coupling between a Cu 3d hole and a core hole, and the anisotropic hybridization between the 3d hole and O 2p valence band holes. As a result, we show that the multiplet structure is strongly affected by the anisotropic hybridization. We discuss the local electronic structures around the Cu atom by analyzing the deviation of the core-level XPS in these materials from the XPS in free Cu²⁺ ion.