The invention relates to rope gripping member for a rope gripping device, the rope gripping member comprising an elongated rope gripping face for being pressed against an elongated side face of an end section of a rope, the elongated rope gripping face having a longitudinal direction and a front edge and a rear edge; wherein tensile stiffness of the rope gripping member in longitudinal direction of the gripping face increases non-linearly with accelerating rate from the front edge towards the rear edge of the gripping face. The invention also relates to a rope gripping device, a rope terminal arrangement and a hoisting apparatus implementing the rope gripping member.