The mechanical nonlinear behaviour of metallocene- and Ziegler-Natta catalyzed polyethylenes with various contents of short chain branching was investigated using a nonlinear constitutive equation in which the plastic deformation and the anharmonicity of elastic response are taken into account. It is suggested that the mechanical behaviour is governed by the plastic deformation for the Ziegler-Natta catalyzed polyethylenes, whereas the anharmonicity strongly affects the mechanical behaviour for metallocene-catalyzed polyethylenes.