In Minimally Invasive Surgery (MIS) the continuously increasing use of robotic devices allows surgical operations to be conducted more precisely and more efficiently. Safe and accurate interaction between robot instruments and living tissue is an important issue for both successful operation and patient safety. Human tissue, which is generally viscoelastic, nonlinear and anisotropic, is often described as purely elastic for its simplicity in contact force control design and online computation. However, the elastic model cannot reproduce the complex properties of a real tissue. Based on in vitro animal tissue relaxation tests, we identify the Hunt-Crossley viscoelastic model as the most realistic one to describe the soft tissue's mechanical behavior among several candidate models. A force control method based on Hunt-Crossley model is developed following the state feedback design technique with a Kalman filter based active observer (AOB). Both simulation and experimental studies were carried out to verify the performance of developed force controller, comparing with other linear viscoelastic and elastic model based force controllers. The studies and comparisons show that the Hunt-Crossley model based force controller ensures comparable rise time in transient response as the controller based on Kelvin-Boltzmann model which is reported as the most accurate description for robot-tissue interaction in recent literature, but it causes much less overshoot and remains stable for tasks with faster response time requirements.