State-of-the-art Additive Manufacturing processes such as three-dimensional (3D) inkjet printing are capable of producing geometrically complex multi-material components with integrated elastomeric features. Researchers and engineers seeking to exploit these capabilities must handle the complex mechanical behavior of inkjet-printed elastomers and expect a lack of suitable design examples. We address these obstacles using a pneumatic actuator as an application case. First, an inkjet-printable actuator design with elastomeric bellows structures is presented. While soft robotics research has brought forward several examples of inkjet-printed linear and bending bellows actuators, the rotary actuator described here advances into the still unexplored field of additively manufactured pneumatic lightweight robots with articulated joints. Second, we demonstrate that the complex structural behavior of the actuator’s elastomeric bellows structure can be predicted by Finite Element (FE) simulation. To this end, a suitable hyperviscoelastic material model was calibrated and compared to recently published models in a multiaxial-state-of-stress relaxation experiment. To verify the material model, Finite Element simulations of the actuator’s deformation behavior were conducted, and the results compared to those of corresponding experiments. The simulations presented here advance the materials science of inkjet-printed elastomers by demonstrating use of a hyperviscoelastic material model for estimating the deformation behavior of a prototypic robotic component. The results obtained contribute to the long-term goal of additively manufactured and pneumatically actuated lightweight robots.