Shape memory polymers (SMPs) have the capacity to store and recover relatively large strains when subjected to a unique thermomechanical cycle. In this study, the thermomechanics of strain storage and strain/stress recovery are investigated in a shape memory polymer deformed under uniaxial tension and compression. During heated recovery, three cases of constraint are examined: unconstrained (free) strain recovery, stress recovery under pre-strain constraint, and stress recovery under fixed-strain constraint. Based on the experimental results, a one-dimensional SMP constitutive model is developed, which is motivated by the shape memory mechanism of the polymer network. The foundation of the model is that the entropy change is gradually stored during cooling and released during reheating as free recovery strain or constrained recovery stress. When fit to free strain recovery data, the model can predict the trends of the stress evolution during shape fixation and constrained strain/stress recovery under various thermomechanical conditions.