The logarithmic strain is more suitable for analyzing large strain problems because the volume invariability condition in small deformation is equivalent to volume invariability condition in large deformation when using the logarithmic strain. Large simple shear deformation has always been used in the analysis of large strain problems. In this paper, elastic large strain constitutive model was introduced based on the logarithmic strain and large simple shear deformation was analyzed by using the constitutive model given in the paper. The stress responses to large simple shear deformation were derived corresponding to four objective rates of tensors. The results show that normal stresses may maintain good monotonicity, but there exists different levels of oscillation of shear stress corresponding to various objective rates, and there was the most severe oscillation of stress when adopting Jaumann rate. The objective rate should not be the only factor bringing about oscillation of shear stress.