Continuum robots are a unique type of robots that move due to the elastic deformation of their own body. Their flexible design allows them to bend at any point along their body, thus making them usable in workspaces with complex geometry and many obstacles. Continuum robots are used in industry for non-destructive testing and in medicine for minimally invasive procedures and examinations. The kinematics of continuum robots consisting of a single bending section are well known, as is the forward kinematics for multi-section continuum robots. There exist efficient algorithms for them. However, the problem of inverse kinematics for multi-section continuum robots is still relevant. The complexity of the inverse kinematics for multi-section continuum robots is quite high due to the nonlinearities of the robots’ motion. The article discusses in detail the modification of the FABRIK algorithm proposed by the authors, as well as a Jacobian-based iterative algorithm. A comparison of inverse kinematics algorithms for multi-section continuum robots with constant section length is given and the results of the experiment are described.