In　this　paper,　a　two　layers　carbon　fiber　reinforced　resin　matrix　trapezoidal　bi-stable　composite　laminate　plate　with　unsymmetric　cross-ply　is　considered.　It　is　assumed　that　the　trapezoidal　bi-stable　composite　laminate　plate　is　fixed　at　origin　point,　and　the　four　boundaries　are　free.　In　order　to　obtain　the　stable　configurations　and　the　natural　frequencies　of　the　trapezoid　bi-stable　composite　laminate　plate　with　the　given　boundary　condition,　a　set　of　polynomial　displacement　functions　including　17　coefficients　is　employed　to　express　the　displacements.　By　using　the　classical　laminate　plate　theory,　von　Karman　nonlinear　geometric　relationship,　minimum　potential　energy　principle　and　Newton　Raphson　iterative　method,　the　stable　configurations　of　the　trapezoidal　bi-stable　laminate　plate　are　obtained.　The　calculation　of　stable　configurations　is　verified　by　comparing　the　classical　results　with　the　present　equilibrium　solution　curves.　Then,　with　the　help　of　continuous　algebraic　polynomial　functions,　Lagrange　multiplier　method　and　Rayleigh–Ritz　method,　the　natural　frequencies　are　computed.　After　verification,　the　influences　of　different　geometric　parameters　and　layering　angle　on　the　natural　frequency　are　researched　in　detail.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.