Motion planning and redundancy resolution of a multi-segment continuum robot is studied. The direct and inverse kinematics model of the robot is derived assuming a constant radius of curvature in each flexible segment of the robot. Due to the primary and secondary backbone structure of the segment, each segment is modelled by two configuration variables and three joint space variables. This introduces both kinematics and actuation redundancy in the system. Kinematic redundancy of the robot is resolved through a closed loop Jacobian pseudo inverse technique, completed with the damped least square technique for singularity robustness provision. Furthermore, an improved Jacobian based motion planning is introduced which optimizes a predefined cost function corresponding a given secondary task. The methods are implemented both numerically and experimentally and accuracy and errors of the results are analyzed.