The micro-diffusion equation for Zener pairs and asymmetric pairs of point defects in fcc metals under the action of periodic distributional moving sources of inner stress have been solved by using finite Fourier transformation and Laplace transformation. Finite sum formulae for rigidity and damping coefficient of a kink have been obtained.Numerical results are given. A simple analytic result is obtained for anelastic interaction between edge dislocation and asymmetric pairs of point defects, which is found to be in agreement with other results based on a different approach.The enhanced internal friction due to the interaction between dislocation and point defects is discussed.