Traditional magnetic resonance elastography (MRE) applies small amplitude vibration to tissues. Thus currently MRE measures only the small deformation behaviour of tissues. MRE has the potential to estimate the strain-varying shear modulus of soft tissues, if applied at different static strains, which may allow prediction of the large-strain behaviour of tissues. This study uses MRE of bovine liver specimens under various levels of static compressive pre-strain up to 30%. Storage and loss moduli measured using MRE increased non-linearly with static compressive pre-strain, and exponential models fit well to these data to describe this relationship (R 2>0.93). Based on these models, a 10% linear compression of liver would result in a 47% overestimate of the 'true' storage modulus of the uncompressed tissue. The results of this study have implications for MRE transducer design and interpretation of results from in vivo MRE studies.