The　research　gradually　highlights　vibration　and　dynamical　analysis　of　symmetric　coupled　nonlinear　oscillators　model　with　clearance.　The　aim　of　this　paper　is　the　bifurcation　analysis　of　the　symmetric　coupled　nonlinear　oscillators　modeled　by　a　four-dimensional　nonsmooth　system.　The　approximate　solution　of　this　system　is　obtained　with　aid　of　averaging　method　and　Krylov-Bogoliubov　(KB)　transformation　presented　by　new　notations　of　matrices.　The　bifurcation　function　is　derived　to　investigate　its　dynamic　behaviour　by　singularity　theory.　The　results　obtained　provide　guidance　for　the　nonlinear　vibration　of　symmetric　coupled　nonlinear　oscillators　model　with　clearance.