The　bistable　asymmetric　composite　laminated　structures　have　the　broad　applications　in　the　design　of　the　deformable　aircrafts　and　energy　harvester　due　to　the　unique　nonlinear　dynamic　snap-through　characteristics.　This　paper　studies　the　dynamic　snap-through　phenomena　and　nonlinear　vibrations　of　the　bistable　asymmetric　cross-ply　composite　laminated　cantilever　shell　under　the　external　excitation.　Reddy＇s　third-order　shear　deformation　theory　and　Hamilton　principle　are　applied　to　establish　the　differential　dynamic　governing　equation　of　the　bistable　asymmetric　composite　laminated　cantilever　shell.　Two-degree-of-freedom　nonlinear　dynamic　system　is　obtained　by　employing　Galerkin　approach.　The　curvature-displacement　relationship　is　given　for　the　bistable　asymmetric　composite　laminated　cantilever　shell.　Chebyshev-Ritz　is　utilized　to　obtain　both　natural　frequencies　and　mode　shapes　of　the　bistable　asymmetric　composite　laminated　cantilever　shell.　Considering　the　cantilever　boundary　condition,　the　free　vibrations　are　analyzed　by　considering　different　factors　of　the　bistable　asymmetric　composite　laminated　cantilever　shell,　such　as　the　curing　temperature,　numbers　of　the　layers　and　geometry　parameters.　It　is　observed　that　the　dynamic　snap-through　behaviors　and　chaotic　vibrations　are　found　under　varying　the　frequency　and　amplitude　of　the　external　excitation.　Several　validations　are　carried　out　among　the　obtained　results　with　these　of　other　references.　The　results　of　the　numerical　simulation　and　finite　element　software　ABAQUS　are　in　good　agreement　with　these　of　the　vibration　experiment.　©　2023　Elsevier　Ltd