Abstract: Active control of the undesired vibrations of manipulators is still an open research issue and has critical relevance for the robots employed in surgical operations, where a primary goal is getting safe, accurate and repeatable positioning. This work, comprising two companion papers, proposes two control schemes that have been designed to achieve satisfactory performance in the position and vibration control of two closed-chain planar manipulators with flexible links. The control schemes have been designed, tuned and tested in simulation, where the dynamic behaviors of the flexible manipulators have been reproduced through a fully coupled nonlinear model based on the finite element theory. Part I of the paper presents the model adopted and the characteristics of the manipulators used as test cases, while the synthesis of the regulators and the numerical results are described in Part II.