To identify the behavior of viscoelastic fluids at small deformations proposed linear dynamic neural network model. The model implements the principle of adaptive hierarchical settings. To achieve a given level of error identification (10-12) model automatically changes its structure from the third to the 24th order of complexity. Neural network model is compared to the known phenomenological models of viscoelastic media has more speed, it allows the use of parallel algorithms for calculating and automatically implements adaptive hierarchical principle of construction. Small error learning linear time-dependent dynamic model without feedback is attainable only if a sufficiently large source of experimental data.