A constitutive model is derived for the physical aging of amorphous polymers. The model is based on the concept of transient networks, where a viscoelastic medium is treated as a system of adaptive links which break and arise due to micro-Brownian motion. Loss and reformation rates for the adaptive links are assumed to depend on the free volume fractions which, in turn, are governed by some kinetic equations. The model permits the long-term viscoelastic behaviour to be predicted based on experimental data obtained in standard short-term creep and relaxation tests. To verify the constitutive equations, we compare results of a numerical simulation with experimental data for several polymers, and demonstrate fair agreement between observations and their prediction.