This paper deals with studying and developing a proper constitutive model for liver tissue. For this purpose, deformation of liver in uniaxial compression, for two different strain rates, is analytically and numerically studied, based on both hyperelastic and hyperviscoelastic constitutive models. Both of the models are based on a polynomial-form energy function. The stress-strain curves, for uniaxial compression, obtained from these models, have been fitted to the existing experimental data to determine the model coefficients. Moreover the models are examined in uniaxial tension and pure shear loadings. ABAQUS commercial software, in which both of the models are available, has been used for numerical simulations. Then, to evaluate the computational analyses, analytical and numerical results have been compared with each other and also with the existing experimental data. The results show that the presented analytical solution and FE simulation are very close together and also both are accurate enough, compared with the experimental data and an acceptable stability is observed. Furthermore the effect of friction coefficient between the sample and the compressing plate in uniaxial compression test has been investigated. FE simulation results show that the stress will increase with increasing friction coefficient. This implies that friction coefficient must be carefully selected to accurately describe the tissue’s response. Compared with previously published researches on other tissues, the constitutive models adopted here to predict liver behavior is mathematically more complex due to non-zero material constants. Analytical solution of these constitutive models is, in fact, the main challenge and innovation of this paper.