The paper presents a study and justification of the concrete creep computational model for use in computer calculations of concrete and reinforced concrete structures of arbitrary complexity, with a possible change in the intensity of the current load over time. The computational model is based on the generalized Maxwell-Wiechert model of the viscoelastic material. The model was verified on the basis of data from experimental studies of concrete creep, was justified and calibrated in accordance with the requirements of regulatory documents for calculations of concrete and reinforced concrete structures, taking into account the material creep. The paper focuses on the situation where the creep of the material leads to a dangerous change in the structural scheme of a building, which in turn can cause its destruction. Verification of the creep computational model and calculation of structures using the selected computational model was carried out in the SIMULIA Abaqus software environment. © Published under licence by IOP Publishing Ltd.