Concrete creep is a complex physical phenomenon and has different characteristics from those observed in most materials. Despite several studies developed, the understanding of this phenomenon is not yet complete and the models available in the literature for numerical simulation vary in complexity, number of parameters and conditions that ensure their applicability. The latest studies developed by Bazant stand out and report good agreement with experimental results. Their fundamentals are used in the development of the linear basic creep model adopted in this work. Thus, it is carried out a review of linear viscoelasticity, in which the rheological models, the constitutive relationships, and the main assumptions adopted in the multi-axial state of stress are presented. Concrete creep properties are discussed and the solidification theory is presented, aiming to represent the development over time of the apparent concrete properties. Based on this study, a basic creep model with aging defined by Kelvin chains is adopted and an algorithm for numerical integration of the strain rate is developed. The model is implemented in a finite element program and validated with experimental linear creep results. Finally, this work proposes modeling the nonlinear dependence of concrete creep with the use of cohesive interface elements. A methodology for calibrating the parameters involved is presented, and the model response is compared with the experimental results of a bending creep test. The numerically obtained results show good agreement with the experimental results for both the pure linear creep and the creep and damage.