Abstract: Against the viscoelastic encapsulation induced thickness uniformity controlling technical problems of composite coextruded products, the influencing rule and mechanism of viscoelastic rheological parameter on polymer co-extrusion viscoelastic encapsulation were studied by the numerical simulation. Research results show that the viscoelastic encapsulation is induced by the second normal stress difference driven secondary flow in co-extrusion multiphase stratified flows, and depends on the direction and strength of melt secondary flow. The direction of melt secondary flow depends on the sign of secondary normal stress difference, and its strength is proportional to secondary normal stress difference. The viscoelastic encapsulation increases with increasing of polymer melt relaxation time. The theoretical premise of eliminating viscoelastic encapsulation is elimination of the secondary flow in co-extrusion multiphase stratified flows, and the secondary flow can be eliminated by means of making the second normal stress difference tend to zero. The transformation of the no-slip adhesive coextrusion multiphase stratified shear flow into the full-slip non-adhesive gas assisted coextrusion multiphase stratified plug flow is the theoretical prerequisite of making the second normal stress difference tend to zero, and the air cushion wall full slip of gas-assisted co-extrusion molding process is an effective technique to achieve this transformation.