We　present　the　analysis　of　codimension-3　degenerate　bifurcations　of　a　simply　supported　flexible　beam　subjected　to　harmonic　axial　excitation.　The　equation　of　motion　with　quintic　nonlinear　terms　and　the　parametrical　excitation　for　the　simply　supported　flexible　beam　is　derived.　The　main　attention　is　focused　on　the　dynamical　properties　of　the　global　bifurcations　including　homoclinic　bifurcations.　With　the　aid　of　normal　form　theory,　the　explicit　expressions　of　normal　form　associated　with　a　double　zero　eigenvalues　and　Z2-symmetry　for　the　averaged　equations　are　obtained.　Based　on　the　normal　form,　it　has　been　shown　that　a　simply　supported　flexible　beam　subjected　to　the　harmonic　axial　excitation　can　exhibit　homoclinic　bifurcations,　multiple　limit　cycles,　and　jumping　phenomena　in　amplitude　modulated　oscillations.　Numerical　simulations　are　also　given　to　verify　the　good　analytical　predictions.