Steerable concentric continuum robots are robots with a flexible structure that are able to bend at any point. Such robots consist of tubes inserted inside each other. The shape and length of the robot can be varied by controlling relative translations, rotations and bending angles of the tubes. This feature allows them to operate in confined working areas such as human heart, lungs, nuclear reactors and so on. However, existing solutions to the inverse kinematics for these robots have the following problems: high computational cost, singularity problems, complex matrix calculations, inability to control a robot tip orientation or requirement to go through the configuration parameters. This paper presents a modification of the Forward And Backward Reaching Inverse Kinematics (FABRIK) algorithm for multi-section continuum robots. Particularly, we applied the proposed modification of the FABRIK algorithm to the steerable concentric continuum robots.