The shape-memory effect (SME) in polymers is a stimuli-responsive feature that is attracting more and more attention, thanks to its usage in fields ranging from the biomedical sector to soft robotics. The two-way SME, in particular, has great potential for applications needing repeated cycling, e.g., actuators, and motivates the development of theoretical and numerical tools to support their design. The present paper aims to propose a onedimensional finite-strain phenomenological model to describe the one-way SME as well as the two-way SME under stress conditions in thermo-responsive semi-crystalline crosslinked polymers. The model is simple, easy to implement, and based on parameters with a clear and direct physical interpretation and measurability. Model predictions are validated on experiments on semi-crystalline networks based on poly(epsilon-caprolactone) and demonstrate model ability in describing several material features as the effect of the crosslink density on SME, the dependence of microstructural evolution on applied load and heating/cooling rate, and the presence of thermal strains.