Physically-based methods ensure an accurate simulation of the realistic behavior of virtual 3D objects. In this paper, we define a novel approach to use tangible user interaction combined with a mechanical solver for simulating physically-based deformations. The user directly controls the resulting geometry of the virtual 3D object by means of intuitive two-handed manipulations of a deformable input device. We describe the simulation steps and address the difficulties related to the communication between the three main components: the input device, the virtual 3D object, and the physical solver. We present a prototype framework for running bending and twisting beam deformations. In particular, we explore the potential of the ShapeTape, a sensitive malleable strip, as input peripheral for controlling the user interactions. Our work is an excellent educational tool for understanding mechanical phenomena. It is also applicable in an archaeological context in order to understand the chronology of the different deformations that were suffered by archeological findings.