The　occurrence　conditions　of　the　metastable　chaotic　vibrations　are　firstly　studied　in　the　bistable　asymmetric　composite　laminated　square　shallow　shell　under　the　foundation　excitation.　The　metastable　chaos　is　observed　in　the　vibration　experiments　of　the　bistable　asymmetric　composite　laminated　square　shallow　shell.　Based　on　the　dynamic　model　of　the　bistable　asymmetric　composite　laminated　square　shallow　shell,　the　critical　instability　condition　of　the　zero　equilibrium　point　is　analyzed　in　the　bistable　asymmetric　composite　laminated　square　shallow　shell　by　using　Jacobian　matrix　and　Routh-Hurwitz　criterion.　We　perform　numerical　simulations　based　on　Runge-Kutta　algorithm　and　the　vibration　experiments.　A　sufficient　condition　is　found　for　the　existence　of　the　metastable　chaos　in　the　bistable　asymmetric　composite　laminated　square　shallow　shell.　It　is　found　that　the　zero　equilibrium　point　of　the　bistable　asymmetric　composite　laminated　square　shallow　shell　is　unstable　when　the　parametric　excitation　exceeds　a　specific　critical　value.　The　numerical　results　verify　the　theoretical　analyses　of　the　metastable　chaos.　It　is　demonstrated　that　the　increase　of　the　parametric　excitation　leads　to　the　easier　occurrence　of　the　metastable　chaos　through　observing　the　characteristics　of　the　nonlinear　dynamic　behaviors　of　the　system.　Moreover,　the　existence　of　the　metastable　chaotic　vibrations　is　confirmed　in　the　bistable　asymmetric　composite　laminated　square　shallow　shell　under　the　foundation　excitation　by　using　the　vibration　experiments.　The　large　parametric　excitation　subjecting　to　the　bistable　asymmetric　composite　laminated　square　shallow　shell　is　a　key　factor　for　the　existence　of　the　metastable　chaos　in　the　bistable　asymmetric　composite　laminated　square　shallow　shell　under　the　foundation　excitation.　©　2020　Elsevier　Ltd