Shape memory polymers (SMPs) have been intensively studied for a wide range of potential applications, including biomedical devices, morphing structures, and 4D printing. For amorphous polymers, the glass transition temperature measured by dynamic mechanical analysis (DMA) is an important consideration in designing SMPs. However, typical DMA curves are cooling- and heating-rate dependent and the cooling and heating traces for storage modulus form a (sometimes large) hysteresis loop. This paper first experimentally studies temperature-rate effects on DMA results. A constitutive relation is then developed based on the assumption that the stress relaxation behavior depends on both temperature and structural relaxation state. Good agreement is obtained between the experimental and the modeling results. This model is then applied to study the shape memory behaviors, showing that structural relaxation plays an important role in the free recovery; the model without considering structural relaxation tends to predict a fast recovery. (C) 2016 Published by Elsevier Ltd.