There is considerable experimental evidence that the classical no-slip boundary condition of fluid mechanics is not always a valid assumption for the flow of high molecular weight molten polymers. In fact, molten polymer slip solid surfaces when the wall shear stress exceeds a critical value. Moreover, there exists a second critical wall shear stress value at which a transition from a weak to a strong slip takes place. The later corresponds to the case of an almost plug flow and it is accompanied by pressure oscillations in the case of capillary,flow,generated by a constant-speed piston-driven capillary rheometer. The two modes of slip (weak and strong) are due to flow-induced chain detachment/desorption directly from the polymer/wall interface and to chain disentanglement of the polymer chants in the bulk from a monolayer of polymer chains adsorbed at the interface. In this work, the two physical mechanisms of slip are discussed and validated on the basis of suitably analyzed experimental data. Based on these buy modes of slip, the slip phenomena observed during the capillary flow of polymers (mainly polyethylenes) are explained including the absence of pressure oscillations in the capillary flow of branched polyethylenes.