The present work deals with experimental and numerical features of entry flows of two polyethylene melts, namely a linear low-density polyethylene (LLDPE) and a low-density polyethylene (LDPE) in an axisymmetric converging geometry. The study also involves rheological characterization of the polymers and determination of flow parameters, at 160 degrees C. For both fluids, the data are fed into a viscoelastic integral Wagner constitutive equation. Tile numerical flow simulations are performed by using a stream-tube mapping analysis. Consideration of a sub-do-main of the total flow domain, the ＇＇peripheral stream tube＇＇, close to the wall of the converging duct permits to relate the results of the numerical simulation to experimental flow characteristics as total and entrance pressure drops. The agreement is good for the total pressure losses, but, concerning LDPE, a lack of consistency remains for the entrance pressure drop.