This article presents the design of soft material robots with tunable damping properties. This study derives from the investigation of an under-actuated dynamic approach involving multi-chamber pneumatic systems. The co-design of the mechanical parameters (stiffness and damping) of the system along with the time profile of the input allows to obtain different behaviors using a reduced number of feeding line. In this work we analyze via simulations and experiments several approaches to tune the damping of soft robots. The most effective solution employs a layer of granular material immersed in viscous oil within the chamber wall. This method has been employed to realize bending actuators with a continuous deformation pattern. Finally, we show an application involving a two-fingered gripper fed by a single pneumatic line, which is able to perform pinch and power grasp.