Non-Gaussian　processes　beset　many　aspects　of　structural　engineering　analysis.　To　estimate　non-Gaussian　processes,　various　third-order　Hermite　polynomial　models　have　been　proposed　and　widely　applied.　Different　forms　of　expressions　have　been　proposed　for　hardening　and　softening　processes　in　existing　Hermite　polynomial　models,　which　makes　them　inconvenient　to　implement.　Furthermore,　these　models　are　either　too　simple　to　ensure　accurate　results　or　too　complicated　to　implement　conveniently.　Thus,　a　unified　third-order　Hermite　polynomial　model　that　achieves　a　good　balance　between　accuracy　and　convenience　for　both　hardening　and　softening　processes　is　proposed　in　this　study.　Explicit　expressions　for　translations　of　the　marginal　distributions　between　the　non-Gaussian　and　Gaussian　processes　using　the　proposed　Hermite　polynomial　model　are　deduced,　and　the　applicable　ranges　are　provided.　The　accuracy　of　the　proposed　model　is　demonstrated　by　comparing　the　coefficients　and　estimated　moments　with　those　obtained　from　the　moment-matching　method.　Furthermore,　the　application　of　the　proposed　model　in　evaluating　first　passage　probability,　analyzing　fatigue　damage,　and　estimating　peak　factors　of　non-Gaussian　wind　pressure　coefficient　histories　is　demonstrated　with　numerical　and　practical　examples.