A theory of mechanical damping based on the model developed by Granato and Lu¨cke was extended to small numbers of pinning points per network length and to stresses high enough to produce complete breakaway. The detailed response of a dislocation array to an applied stress was calculated using computer techniques in the low‐frequency (kilocycle) range and both the viscous and hysteretic damping were computed. The amplitude dependence of the viscous and hysteretic damping was computed as a function of loop‐length distribution, distribution of dislocation orientations, pinning point density, and stress distribution. The computation techniques allowed these calculations to be made without the usual mathematical approximations which are shown to result in a severe limitation on the previous analytic expressions. The results were applied to a discussion of the use of the damping theory to obtain parameters which describe the dislocation array and dislocation behavior. The time dependence of dislocation damping which results from diffusion of pins along the dislocation and in the lattice is discussed.