We performed an analysis of post-seismic stress relaxation, taking into account generalized linear rheologies. We compared the stress field (and its derived functions) obtained with a classical Maxwell rheology with that obtained with a transient Burgers body. From a set of synthetic case studies, we have revealed quantitative and qualitative differences both in relaxation times and in local stress values when a transient rheology is introduced. As a practical application, we modeled the time evolution of the Coulomb failure function following the 2009 L'Aquila earthquake, and we show that a transient rheology can lead to non-monotonic time dependence.