The　probability　distribution　problem　of　the　steady-state　responses　to　horizontal　and　vertical　Gaussian　white　noises　of　rigid　sliding　structures　with　hardening　restoring　force　is　studied　in　this　paper.　The　original　system　is　substituted　by　the　one　with　equivalent　linear　restoring　force,　and　the　analytic　solution　of　the　joint　probability　density　of　the　steady-state　responses　of　the　equivalent　system　is　derived　by　means　of　the　equivalent　nonlinear　system　method.　The　applicability　of　the　present　method　in　the　paper　is　exemplified　by　the　results　of　Monte　Carlo　simulation.