A flexible surgical robot that can adjust its stiffness guarantees safe operation by satisfying both the high flexibility required when the robot approaches a surgical target and the more stiffness necessary for the end effector to perform surgical procedures. Therefore, this paper proposes a flexible surgical robot that consists of a central backbone, eight super-elastic wires as peripheral backbones, SMA springs, rubber tubes, and several disks. The inner diameter of the SMA springs that can be changed via their temperature creates a tightening force change to apply onto the eight backbone wires of the robot to adjust the overall stiffness of the robot. The simple structure is favorable for robot miniaturization. Frictional force and stiffness modulation experiments of the robot are performed. The results confirmed that the robot's stiffness was increased approximately 1.4 times between the martensite state and the austenite state of the SMA spring. The relationship model between the flexural rigidity of the robot and the frictional force between the SMA spring with the peripheral backbones is established. We compared the flexural rigidity values obtained from our model with those of the experimental result and confirmed that the model was valid.