In this paper, we propose a new continuum robotics approach for haptic rendering and co-manipulation. This approach is illustrated using a robotic interface with 6 motorized fixed axes connected by deformable beams, in parallel, to an end-effector with 5 degrees of freedom (DOF). Apart from the rotation of the motors, this design has no articulation, and the motion of the end-effector is achieved by deformation of the beams. The flexible beams are equipped with bending sensors, and the motors have encoders. We use a non-linear finite element mechanical model of the robot based on a mesh of beam elements that is computed in real time at 20 Hz. The bending sensors are incorporated into the model which allows us to obtain an accurate estimate of the force exerted by the user on the end-effector. The model enables a new methodology for calculating the workspace of the continuum haptic device. The model also is propagated to a higher frequency loop (500 Hz) which performs sensing and control of the robot at high rates, using an admittance-type control to command new positions of the actuators. We show that this control methodology allows haptic rendering of virtual walls that are stiffer than the natural stiffness of the robot. Finally, we demonstrate use of the device for simple co-manipulation tasks.