The experiment of acoustic emission (AE) on concrete specimens under uniaxial cyclic loading was conducted. The Kaiser effect of acoustic emission in concrete and the Felicity effect, which manifest the memorizing ability to the maximum previous stress level of Kaiser effect, were validated by the experiment. The mechanism of Felicity effect was analyzed based on the theory of statistical damage mechanics and a tentative AE factor constitutive model of brittle material under uniaxial cyclic loading was suggested. The curve of constitutive model is in good coincidence with the curve from the experiment. The experimental results showed that the Felicity effect became clearer along with the increasing of stress level. Each loading cycle would cause new damage inside the material, and the response of material to the new loading cycle is different from the previous cycle.