While the effect of normal compression on the measured shear material properties of viscoelastic solids has been already acknowledged in rheological studies in the literature, to our knowledge, no systematic study has been conducted to investigate this effect in detail to date. In this study, we perform two sets of experiments to investigate the effect of normal strain and strain rate on the dynamic shear moduli of bovine liver. First, we apply normal compressive strain to the cylindrical bovine samples up to 20% at loading rates of v=0.000625, 0.00625, 0.0625, 0.315, 0.625 mm/s. Second, we perform torsional shear loading experiments, in the frequency range of ω=0.1-10 Hz, under varying amounts of compressive pre-strain (ε=1%, 2.5%, 5%, 7.5%, 10%, 12.5%, 15%, 17.5% and 20%) applied at the quasi-static loading rate of v=0.000625 mm/s. The results of the experiments show that the shear moduli of bovine liver increase with compressive pre-strain. A hyper-viscoelastic constitutive model is developed and fit to the experimental data to estimate the true shear moduli of bovine liver for zero pre-compression. With respect to this reference value, the mean relative error in the measurement of shear moduli of bovine liver varies between 0.2% and 243.1% for the compressive pre-strain varying from ε=1% to 20%. The dynamic shear modulus of bovine liver for compressive pre-strain values higher than ε>2.5% are found to be statistically different than the true shear moduli estimated for zero compressive strain (p<0.05).