A　surge　in　EVs　is　bound　to　greatly　impact　on　urban　power　grids　and　transportation　networks.　Studying　how　to　accurately　describe　the　impact　of　electric　vehicle　behaviors　on　the　power-transportation　network　is　of　great　significance.　This　paper　considers　the　elasticity　of　demand　for　electric　vehicles　and　their　charging　behaviors　and　introduces　the　quasi-variational　inequalities　(QVIs)　to　address　the　complexity　of　the　game　behavior　modeling　in　the　coupled　network　as　well　as　its　solution　challenges.　First,　a　hybrid　traffic　flow　model　is　built,　which　includes　the　elastic　demand　and　charging　behavior　of　EVs.　On　this　basis,　a　QVI　framework　is　proposed　to　characterize　the　elastic　mixed　user　equilibrium　state,　and　its　equivalence　to　the　equilibrium　state　is　proved.　Secondly,　a　second-order　cone　programming　model　for　the　distribution　network　considering　charging　loads　is　proposed,　and　the　coupling　relationship　between　the　two　networks　is　established.　Then,　the　mechanism　of　the　coupled　network　is　described　as　a　double-layer　game　problem　using　fixed-point　mapping.　Given　the　characteristics　of　inner　and　outer　game　problems,　an　outer　fixed　point　iteration　algorithm　and　an　inner　viscous　projection　approximation　algorithm　are　developed　respectively　to　form　a　complete　method　for　identifying　the　equilibrium　state　of　the　two-layer　game.　The　simulation　based　on　a　test　system　in　Fuzhou　verifies　the　effectiveness　of　the　modeling　and　solving　methods　in　this　paper,　which　shows　the　necessity　of　considering　the　elastic　demand　of　EVs　for　the　equilibrium　state　analysis　of　the　coupled　networks.　©2024　Chin.Soc.for　Elec.Eng.