The aim of this paper is to study the effect of creep loading on damaged multilayered composite cylindrical structure, taking into account various damage rates by developing analytical model. The developed model is used to simulate the elasto-visco-plastic response of damage cylindrical composite structure under different types of loading such as tension and internal pressure with end effect. This model makes it possible to estimate the service life of the multilayed damaged structures subjected to a creep loading. The results obtained make and show that the presence of the damage within the multilayer structures causes a clear increase of the circumferential stress which is the only responsible of the ruin, where some results are compared with experimental testing from previous works and a good correlation is obtained.