The paper presents the results of numerical modeling of concrete rheological manifestations under compression, the properties of which are described by a linear model of a viscoelastic material. The computer model of concrete with viscoelastic properties selected for studies identified by experimental research results of concrete samples. Computer simulation was carried out in a software environment SIMULIA Abaqus. Evaluation of the results of numerical analysis of the concrete elements under the action of constant stress was conducted from their comparison with both the experimental and the normative values of creep strain. The conclusions reached by the results obtained are intended for researchers and designers, performing numerical analysis of concrete and reinforced concrete structures, taking into account creep and relaxation of the material.