The　nonlinear　vibrations　and　dynamic　snap-through　behaviors　are　studied　for　a　four-corner　simply　supported　bistable　asymmetric　laminated　composite　square　shell　under　the　foundation　excitation　by　using　the　theoretical,　Abaqus　finite　element　(FE)　and　experiment　approaches.　The　first-order　shear　deformation　shell　theory　and　Hamilton　principle　are　adopted　to　derive　the　partial　differential　governing　equations　of　motion.　A　novel　type　of　nonlinear　strain-displacement　relations　is　given　by　Sander＇s　strain.　Galerkin　approach　is　utilized　to　discretize　the　partial　differential　equations　of　motion　into　a　three-degree-of-freedom　system.　The　natural　frequencies　and　vibration　modes　of　the　bistable　shell　are　calculated　by　using　Chebyshev　polynomial　method.　The　nonlinear　vibrations　and　dynamic　snap-through　are　investigated　by　using　the　maximum　Lyapunov　exponent,　bifurcation　diagrams,　time　histories,　phase　portraits,　3D　phase　portraits　and　Poincare　maps.　The　theoretical　results　of　the　vibrations　are　well　compared　with　those　of　the　FE　and　experiment.　The　effects　of　the　excitation　and　structural　parameters　on　the　dynamic　snap　through　and　nonlinear　vibrations　are　fully　discussed.　The　influences　of　the　initial　radius　of　the　curvature　on　the　critical　load　of　the　dynamic　snap-through　behaviors　and　rule　of　the　chaotic　vibrations　are　analyzed　for　the　bistable　asymmetric　laminated　composite　shell.