A practical procedure for achieving an, enveloping grasp is presented especially for cylindrical objects. It is composed of three phases, the approach phase, the lifting phase and the grasping phase. For the grasping phase, we introduce the natural computation mode in which a preset torque is commanded to each joint, so that both the equilibrium position and the contact forces may be determined automatically. A sufficient condition for achieving the enveloping grasps is shown for the given procedure. Experimental results are also shown to verify the effectiveness of the proposed grasping procedure.