In view of the automatic manipulation and shaping of rheological objects, e.g. food material or biological tissues, the need of modeling and characterizing the material from an engineering point of view and of constructing a dynamic model of the whole rheological object arise. In this paper, a catenary-like Mass-Spring-Damper (MSD) model formed of lumped masses interconnected with three-element units is proposed to study and simulate the 2-D shaping of a thin rheological material over a moulding object. First, a three-step method for identifying the material properties from experimental tensile tests is proposed and validated. The method has allowed both to identify the material properties and to validate the three-element material model used, thanks to the close agreement between the material mathematical model and the experimental data. Then, a multibody model of the rheological object is proposed, which has been validated thanks to the close agreement between the simulated deformation profile and the experimental one in two test cases: in the first test case the rheological object deforms under the load of the gravity force only, and in the second one it is forced to deform by a shaping tool. Finally, the validated model is used in order to compare different shaping movements and velocities of the tool by dynamic simulations, with particular attention to the internal tensile force generated in the material -which has to be sufficiently far from the break -and the quality of the shaping operation which is directly related to the total non-recoverable deformation generated. A two-step shaping movement results more advantageous with respect to simpler motions since significantly reduced internal forces are generated in the material while the quality of the shaping operation is still guaranteed.