In this paper, the aim is to design and develop a bendable soft actuator prototype to overcome the limitations of Surgical Lighting Systems (SLS). Pneumatic bending actuator made of silicone rubber undergoes the desired deformation when each chamber is pressurized. Surgical luminaires are used for illumination of wounds during surgery. For optimal illumination surgical luminaries need to change their orientation several times during surgery. Soft actuator because of flexibility provides advantage to overcome the mechanical singularity faced by existing surgical lighting system. Mathematical model based on geometric deformation has been presented. A fourth degree polynomial approximation has been used for characterize behavior of each chamber of actuator.