Measuring the viscoelastic behaviour of highly hydrated biological materials is challenging because of their intrinsic softness and labile nature. In these materials it is difficult to avoid pre-stress and therefore to establish precise initial stress and strain conditions for lumped parameter estimation using creep or stress-relaxation tests. We describe a method ($ε$M or epsilon dot method) for deriving the viscoelastic parameters of soft hydrated biomaterials which avoids pre-stress and can be used to rapidly test degradable samples. Standard mechanical tests are first performed compressing samples using different strain rates. The dataset obtained is then analysed to mathematically derive the material's viscoelastic parameters. In this work a stable elastomer, PDMS, and a labile hydrogel, gelatin, were first tested using the $ε$M, in parallel stress-relaxation was used to compare lumped parameter estimation. After demonstrating that the elastic parameters are equivalent and that the estimation of short time constants is more precise using the proposed method, the viscoelastic behaviour of porcine liver was investigated using this approach. The results show that the constitutive parameters of hepatic tissue can be quickly quantified without the application of any pre-stress and before the onset of time dependent degradation phenomena.