A neuronet model of viscoelastic media with associative and inherited memory, which generalizes the known Hopfield neuronet. To train the model it was transferred in the state space where the “input–output” signals were determined explicitly. Tangential stresses in the composite Pi-330 were used as targeted signals. Rectangular pulses of the deformation gradient were used as input signals. The experiments were made using the RS-150 rheoviscosimeter (HAAKE, Germany). As a result of neuronet model training in the regime of finite deformations we found good coincidence between the output and targeted signals. Testing of the trained model on signals not included into the training sampling also showed good agreement of the output signal and the signal obtained experimentally. This indicates that the neuronet model possesses the generalizing property of training massive. Neither integral, nor differential models have this characteristic. It is also shown that the suggested neuronet model of viscoelastic media exactly reproduces a nonlinear dependence of stress on the deformation gradient, which determines the regime of finite deformations.