Handshaking is a fundamental part of human physical interaction that is transversal to various cultural backgrounds. It is also a very challenging task in the field of Physical Human-Robot Interaction (pHRI), requiring compliant force control in order to plan the arm’s motion and for a confident, but at the same time pleasant grasp of the human user’s hand. In this paper,we focus on the study of the hand grip strength for comfortable handshakes and perform three sets of physical interaction experiments between twenty human subjects in the first experiment, thirty-five human subjects in the second one, and thirty-eight human subjects in the third one. Tests are made with a social robot whose hands are instrumented with tactile sensors that provide skin-like sensation. From these experiments, we: (i) learn the preferred grip closure according to each user group; (ii) analyze the tactile feedback provided by the sensors for each closure; (iii) develop and evaluate the hand grip controller based on previous data. In addition to the robot-human interactions, we also learn about the robot executed handshake interactions with inanimate objects, in order to detect if it is shaking hands with a human or an inanimate object. This work adds physical human-robot interaction to the repertory of social skills of our robot, fulfilling a demand previously identified by many users of the robot.