Abstract: An improvement of the creep behaviour prediction of parallel‐lay aramid ropes under varying stresses is the scope of the following study in which application of artificial neural networks (ANNs) for the prediction of creep under varying stresses is presented. This qualitatively different approach assumes that the ANN can be trained to simulate time‐dependent response of the rope in the given load (stress) programme and time interval. The classic rheological constitutive equations are not needed in this case, because ANN acts as a constitutive operator trained by stresses and the corresponding creep strains from experimental data. Carried numerical experiments were divided into the following three parts: (i) searching the best ANN for a creep behaviour approximation under varying stresses, (ii) investigating the best topology of the selected neural network and (iii) investigating the best results for the creep function identification. Comparison between the experimentally observed creep strains of the parallel‐lay aramid rope under varying stresses, predicted creep strains when the linear creep constitutive equation is applied and predicted creep strains when the obtained Jordan neural network with the 3‐10‐1 topology is used confirmed that the Jordan neural network developed achieved less than half mean square error beside the existing creep constitutive analytical approach.