In tissue engineering, mechanical stimulation is used to guide cellular adaptation and tissue development. While a number of bioreactors can apply displacement-controlled strain on scaffolds, emerging evidence suggests that cells respond more to stress rather than strain. In this study, we assess the limitations of displacement-controlled stimulation and investigate an approach of stress control in bioreactors. In our application, the MagneTissue bioreactor applies strain to fibrin rings, which serve as cell scaffolds for tendon tissue modeling. Due to the displacement-controlled nature of the system, the resulting forces and stresses after applying strain remain unknown. It is also unknown, how stresses evolve over time and how relaxation of the scaffold affects the mechanical stimulus on cells. To address these limitations, one of the bioreactor’s loading protocols was replicated on a universal testing setup in a PBS bath, measuring the mechanical response of fibrin rings without cells. The results show that stiffness, expressed as the experienced stress after applying a strain of 20 %, varies for fibrin rings. Additionally, stress relaxation, stress recovery and plastic deformation of the fibrin constructs are observed. A model consisting of Maxwell bodies in parallel is used to describe the mechanical behavior of the ring constructs. This model can be used to predict stresses experienced in the bioreactor. Hence, strain protocols can be adjusted to control stresses within the scaffold and counteract its viscoelastic behavior. This approach aims to enhance bioreactor precision and optimize mechanical stimulation protocols for better control of cell growth.