The implementation of robotic systems for minimum invasive surgery and medical procedures is an active topic of research in recent years. One of the most common procedures is the palpation of soft tissues to identify their mechanical characteristics. In particular, it is very useful to identify the tissue stiffness or equivalently its elasticity coefficient. This identification relies on the existence of a force sensor or a tactile sensor mounted at the tip of the robot, as well as on measuring the robot velocity. For some applications it would be desirable to identify the biomechanical characteristics of soft tissues without the needing of a force/tactile nor velocity sensors. An estimation of such quantities can be obtained by a model-based state observer for which the inputs are only the robot joint positions and its commanded joint torques. The estimated velocities and forces can then be employed for closed-loop force control, force reflection, and mechanical parameters estimation. A closed-loop force control is proposed based on the estimated contact forces to avoid any tissue damage. Then, the information from the estimated forces and velocities is used in a least squares estimator of the mechanical parameters. Moreover, the estimated biomechanical parameters are employed in a Bayesian classifier to provide further help for the physician to make a diagnose. Researchers have found that a combination of the parameters of both a linear and a nonlinear viscoelastic models provide better classification results: 0% misclassifications against 50% when using a linear model, and 3.12% when using only a nonlinear model, for the case in which the samples have very similar mechanical properties.