We　aim　to　study　nonlinear　dynamics　of　a　shell-shaped　workpiece　during　milling　processes　in　this　paper.　The　shell-shaped　workpiece　is　modelled　as　a　cantilever　thin　shell　subjected　to　a　cutting　force　with　time-delay　effects.　The　formulas　of　the　cantilever　shell　were　derived　by　the　classical　shell　theory　and　the　von　Kaman　strain-displacement　relations.　The　resulting　differential　equations　are　reduced　to　a　two-degree-of-freedom　nonlinear　system　ordinary　differential　equations　by　applying　the　Galerkin＇s　approach.　The　method　of　Asymptotic　Perturbation　method　is　used　to　obtain　the　averaged　equations,　which　were　dealt　with　the　resonance　cases　of　1:2　internal　resonance　and　principal　parametric　resonance.　Dynamic　behaviors　are　presented　based　on　the　numerical　solutions.　The　results　show　that　different　time-delay　parameters　result　in　periodic　motion,　multiple　periodic　motion,　and　chaotic　motion.