In this paper, we employ Fung's viscoelastic model discussed by Tiezzi and Kao to study the experimental data presented by Sakamoto et al. for grasping viscoelastic objects using a parallel-jaw gripper. The viscoelastic contact modeling presented in this paper is characterized by two separate responses: elastic response and temporal response. Two main and intriguing results were found in the modeling and analysis of experimental data. The first is the consistency on the normalized coefficients for the curve fitting of the temporal response during the relaxation period of the grasping. Such consistency suggests that the proposed model is applicable to the grasping task at hand. The other result is the generic pattern of the elastic response deduced from the experimental data. The pattern of elastic response represents different physical significance of grasping which involves viscoelastic contact interface.