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The modelling and the control of the web handling systems have been studied for a long time; the correct modelling is necessary in order to design a better control system or to experimentally identify the plant parameters. On the web dynamics itself, lumped parametric expressions may be used to designate a web section between two adjacent drive rolls, and there is the necessity to incorporate the property of visco-elasticity to the web. In this paper the lumped model of a new web tension experimental system is updated; the model is based on the conservation of mass, torque balance and viscoelasticity (Voigt approach). The experimental system consists of four sections, each of which is driven by a servomotor with the speed and tension feedback, by using encoders and tension sensors. Usually these kinds of models are developed in the Laplace domain and the block scheme gives a graphic interpretation of the interaction between different sections. The block scheme transformation in a differential equation system in the time domain is considered in this paper; it requires the introduction of nonzero initial condition for the derivative of physical variables. The problem of validation has been dealt with in detail in this paper, simultaneously considering 2 different combinations of input data in open loop and a multivariable optimization method in order to estimate the unknown parameters. The results will show the accuracy of this kind of lumped parameters model for the complex experimental systems and useful information for successively designing an efficient control strategy.