One-way irreversible shape-memory effect (SME) in polymers may be considered as the ability of a material to fix one or more temporary shapes after preceding deformation and to recover its original shape after application of an external stimulus. Recent results have shown that crosslinked semi-crystalline polymers enable not only one-way irreversible SME, but also two-way reversible SME, which is revealed as an anomalous elongation of a specimen under stress during non-isothermal crystallization and subsequent contraction during heating. To date no well based physical theory exists, which is able to explain this phenomenon. The present study deals with theoretical explanation and description of two-way reversible SME in crosslinked semi-crystalline polymers. The proposed approach is based on the theory of the stress-induced crystallization, but allows calculating the free energy change of a sample deformed under constant load and cooled down below crystallization temperature at a constant cooling rate, i.e. in non-isometric and non-isothermal conditions, respectively. The developed theory was confirmed for a covalently crosslinked high-density polyethylene (HDPE). The analysis of the free energy change performed in case of different crosslink density and deformation predicts the possible crystalline structure (extended or folded chain crystals) and orientation of crystals generated at cooling. It is shown that aforementioned anomalous elongation can be observed under certain crosslink density only when the orientation of chain folds in crystal is parallel to the stretch direction or makes a sharp angle with the stretch direction. The stress-strain-temperature relationship derived from the free energy change was used to fit the experimental findings of the temperature dependent strain under load, which were firstly received by the authors for crosslinked HDPE. The fitting curves have shown well conformance with the experimental data.