The effects of dry or saturated state, water–cement ratio, coarse aggregate type and steel fiber on the stress–strain relationship of RAC under cyclic loading were studied. What is more, the characteristics of stress–strain curve, plastic strain, stress degradation and stiffness degradation of RAC under cyclic loading were analyzed. The microstructure of RAC was analyzed. Based on the principle of surface energy, the reason for the decrease in compressive strength of wet concrete was analyzed. In addition, the envelope equation of stress–strain curve under cyclic loading, unloading and reloading curve was established. The test results showed that the peak stress of the envelope line of RAC under cyclic loading was affected by dry or saturated state, water–cement ratio and coarse aggregate type, but the addition of steel fiber could reduce the degradation rate of stress and stiffness of RAC after peak strain. The plastic strain accumulation of RAC before and after the peak stress was quite different, but dry or saturated state, water–cement ratio, coarse aggregate type and steel fiber have no obvious influence on the plastic strain accumulation of RAC. The pores and cracks of RAC provide space and channels for the moisture absorption and water absorption. The Weibull–Lognormal statistical distribution envelope model, unloading curve model and reloading curve model established were in good agreement with the experimental curves. The research results provided a reference for the study of the full curve constitutive model of RAC under cyclic loading.