An epitaxial growth mechanism of oxide superconductor films has been investigated by using computer graphics for the combination of orthorhombic Ba₂YCu₃O_7-x with substrate crystals of SrTiO₃, MgO, and ZrO₂. The (001) plane of Ba₂YCu₃O_7-x has been shown to fit well the (100) plane of these substrate crystals. A crystallographic fit has also been demonstrated between the (110) plane of Ba₂YCu₃O_7-x and the (110) plane of SrTiO₃. Detailed investigation of atomic arrangements has indicated some differences in the ionic interaction at the superconductor-substrate interface among SrTiO₃, MgO, and ZrO₂ substrates. For the combination of the (001) plane of Ba₂YCu₃O_7-x and the (100) plane of SrTiO₃, various layers of Ba₂YCu₃O_7-x and SrTiO₃ are possible to provide arrangements of ions which stabilize the electrostatic interaction at the interface. Although the Ba-O layer of Ba₂YCu₃O_7-x does not provide such a stable interaction with the MgO (100) plane, the Cu-O layer of Ba₂YCu₃O_7-x can favorably interact with the MgO (100) plane. As for ZrO₂ (100) plane, ionic arrangements at the oxide layer is favorable only for the interaction with Y₃₊ layer of Ba₂YCu₃O_7-x while the Zr-O layer of ZrO₂ can interact with both Ba-O layer and Cu-O layer of Ba₂YCu₃O_7-x.