In this work a numerical method to simulate the response of reinforced concrete structures subject to cyclically imposed displacements is proposed. The method consists of a combination of a displacement and load controlled version of the Newton-Raphson iterative technique, used for the loading and the unloading part of the cycles respectively. The whole procedure is combined with a relatively simple concrete model whose only material parameter is its uniaxial compressive strength. The proposed methodology may realistically simulate, in an easy way, the physical process of any experimentally tested RC structure under imposed displacements cycles. The efficiency of the approach is demonstrated through a series of analyses of experimentally tested specimens reported in the literature.