The mechanical induction of specific cell phenotypes can only be properly controlled if the local stimuli applied to the cells are known as a function of the external applied loads. Finite element analysis of the cell carriers would be one method to calculate these local conditions. Furthermore, the constitutive model of the construct material should be able to describe mechanical events known to be responsible for cell stimulation, such as interstitial fluid flow. The aim of this study was to define a biphasic constitutive model for fibrin, a natural hydrogel often used for tissue engineering but not yet thoroughly characterized. Large strain poroelastic and poroviscoelastic constitutive equations were implemented into a finite element model of a fibrin gel. The parameter values for both formulations were found by either analytically solving equivalent low strain equations, or by optimizing directly the large strain equations based on experimental stress relaxation data. No poroelastic parameters that satisfactorily described the fibrin carrier behaviour could be found, suggesting that network viscoelasticity and fluid-flow time-dependent behaviour must be separately accounted for. It was demonstrated that fibrin can be described as a poroviscoelastic material, but a large strain characterization of the parameter values was necessary. The analytical resolution of the low strain poroviscoelastic equations was, however, accurate enough to serve as a reliable initial condition for further optimization of the parameter values with the large strain formulation.