Abstract: In this paper, the change in gravity caused by local deformation of the crustal medium is quantitatively investigated. By the method of point mass displacement (i.e. the Lagrange Method) the integral relation between the displacement field of crustal medium and the additional gravity field involved has been derived.By using known analytic expressions of the displacement due to a slip of a fault of any dipping angle in an elastic or visco-elastie half-space, we have calculated by three-dimensional numerical integration, the additional gravity field on the ground surface, resulting from various types of fault movements in an elastic or genera lized Kelvin medium, as well as the tendency of gravity change with time given rise by the rheological behavior of the medium.Referring to the movement of the Cang-Tong Fault before the Tangshan Earthquake of 1976 and the fault dislocation during that earthquake, the associate gravity change before and after the earthquake has been computed and the results agree to a certain extent with the observed.