In　the　analytical　model　of　eddy-current　(EC)　testing,　the　reflection　coefficient　(RC)　plays　a　crucial　role　in　the　calculation　of　mutual　impedance　and　inductance.　The　RC　describes　the　reflection　characteristics　of　test　pieces　concerning　incident　electromagnetic　waves　and　determines　the　phase　of　EC　signals.　Previously,　the　RC　was　computed　using　analytical　solutions.　However,　obtaining　it　for　test　pieces　with　complex　geometries　proved　challenging,　limiting　its　application,　e.g.,　in　the　calculation　of　defect　signals.　This　study　proposes　a　numerical　solution　to　RC　based　on　the　second-order　vector　potential　(SOVP).　For　metallic　planar　and　cylindrical　structures,　the　RC　solution　is　calculated　using　numerical　methods.　In　numerical　simulations,　the　RC　values　obtained　through　the　proposed　method　align　well　with　analytical　solutions.　When　compared　with　the　finite　element　method　(FEM)　solution　for　coil　inductance,　the　proposed　method　demonstrates　fast　and　accurate　inductance　solutions　for　ferrite-core　coils　used　in　test　pieces　with　defects.