In this paper, a nonlinear latency model is presented to describe the relationship between the strain and strain rate of the temporal responses in robotic grasping that involves viscoelastic contact interface. The results from experiments and simulation are presented, and are found to match well with each other. The nonlinear latency model was able to adequately represent both Type I and Type II relaxation responses. For the successive loading and holding with a soft contact, the model describes the behavior of step-wise increase of equilibrium strain and a polynomial relationship between the strain rate and the strain. The nonlinear latency model can successfully predict and model the behavior of anthropomorphic soft contact interface in grasping and manipulation when the grasped object is held in certain posture of prehension with repeated loading and/or unloading.