We consider the neural network model in the state space to simulate the behavior of viscoelastic fluids, which is a further development of the recurrent model proposed by the authors. The conditions under which the proposed model is controllable and observable. Built learning algorithm models with the teacher, based on the method of back propagation, revised for recurrent neural networks. The results of numerical experiments showing the efficiency of the system and the quality of its training. The dependence of the quality of education systems and the ability to generalize from the scope and quality of the training set.