This paper proposes a cylindrical grip type of tactile device that is effectively integrated to a surgical robot console so that a surgeon can easily touch and feel the same stiffness as the operating organs. This is possible since the yield stress (or stiffness) of magnetic-responsive materials can be tuned or controlled by the magnetic field intensity. The proposed tactile device consists of two main parts: a magnetorheological elastomer (MRE) layer and a magnetorheological fluid (MRF) core. The grip shape of the device to be positioned on the handle part of the master of the surgical robot is configured and its operating principle is discussed. Then, a couple of equations to calculate the stiffness from the gripping force and the field-dependent yield stress of MRF are derived and integrated using the finite element analysis (FEA) model. After simulating the stiffness of the proposed tactile device as a function of the magnetic field intensity (or current), the stiffnesses of various human organs, including the liver and heart, are calculated from known data of an elastic modulus. It is demonstrated from comparative data between calculated stiffness from human tissues and simulated stiffness from FEA that the proposed tactile device can generate sufficient stiffness with a low current level to recognize various human organs which are significantly required in the surgical robot system.