Samples of linear polyethylene, neat and crosslinked by irradiation with electron beam, were subjected to heavy plastic deformation by plane-strain compression up to the true strain exceeding 2 (deformation ratio λ > 8) at room temperature. Structural studies of deformed samples and investigation of long-term strain recovery demonstrated that the deformation of the neat, non-crosslinked HDPE is completely reversible above the melting point of the crystalline phase, provided that the applied true strain does not exceed e = 1.0 (λ = 2.7). At higher applied strains, e > 1, an irreversible deformation component emerged gradually, and at e = 2.1 (λ = 8.2), the permanent, truly irreversible, residual strain was approx. eres = 0.36 (λ = 1.4). In contrast, samples of crosslinked HDPE above Tm exhibited complete reversibility of deformation, irrespectively of an applied strain, and eres ≈ 0. The source of permanent irreversible strain component in neat HDPE is a deformation-induced partial destruction of the molecular network of entangled chains within amorphous interlamellar layers. The principal mechanism found was chain disentanglement, which was supplemented by a very limited chain scission. In the case of crosslinked materials, the dense and relatively homogeneous molecular network appeared robust enough to avoid any damage. Consequently, the strain appeared here fully reversible upon melting of crystalline phase.